Mixing
Finding x and y from two linear equations
Clash Royale CLAN TAG#URR8PPP
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I have two linear equations:
$110x + y = 10$
and
$95x + y = 0$
The solution given in the course I have is $x = 2/3$ and $y = -63.33$
No workings are given.
I am not sure how to solve for $x$ and $y$. I tried rearranging the first equation to find $x$:
$x = 10-y/110$
Then do I substitute this for $x$ into the other equation?
$95 (10-y/110) + d = 10$
Not sure if I'm on the right track.
linear-algebra
asked 2 days ago
axiom111
93
add a comment |Â
up vote
-1
down vote
favorite
I have two linear equations:
$110x + y = 10$
and
$95x + y = 0$
The solution given in the course I have is $x = 2/3$ and $y = -63.33$
No workings are given.
I am not sure how to solve for $x$ and $y$. I tried rearranging the first equation to find $x$:
$x = 10-y/110$
Then do I substitute this for $x$ into the other equation?
$95 (10-y/110) + d = 10$
Not sure if I'm on the right track.
linear-algebra
asked 2 days ago
axiom111
93
What is $d$? Is that $y$?
– Dave
2 days ago
Sorry, yes $d$ is actually meant to be $y$.
– axiom111
2 days ago
I have now corrected this.
– axiom111
2 days ago
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I have two linear equations:
$110x + y = 10$
and
$95x + y = 0$
The solution given in the course I have is $x = 2/3$ and $y = -63.33$
No workings are given.
I am not sure how to solve for $x$ and $y$. I tried rearranging the first equation to find $x$:
$x = 10-y/110$
Then do I substitute this for $x$ into the other equation?
$95 (10-y/110) + d = 10$
Not sure if I'm on the right track.
linear-algebra
asked 2 days ago
axiom111
93
I have two linear equations:
$110x + y = 10$
and
$95x + y = 0$
The solution given in the course I have is $x = 2/3$ and $y = -63.33$
No workings are given.
I am not sure how to solve for $x$ and $y$. I tried rearranging the first equation to find $x$:
$x = 10-y/110$
Then do I substitute this for $x$ into the other equation?
$95 (10-y/110) + d = 10$
Not sure if I'm on the right track.
linear-algebra
asked 2 days ago
axiom111
93
edited 2 days ago
asked 2 days ago
axiom111
93
asked 2 days ago
axiom111
93
asked 2 days ago
axiom111
93
93
What is $d$? Is that $y$?
– Dave
2 days ago
Sorry, yes $d$ is actually meant to be $y$.
– axiom111
2 days ago
I have now corrected this.
– axiom111
2 days ago
add a comment |Â
What is $d$? Is that $y$?
– Dave
2 days ago
Sorry, yes $d$ is actually meant to be $y$.
– axiom111
2 days ago
I have now corrected this.
– axiom111
2 days ago
What is $d$? Is that $y$?
– Dave
2 days ago
What is $d$? Is that $y$?
– Dave
2 days ago
Sorry, yes $d$ is actually meant to be $y$.
– axiom111
2 days ago
Sorry, yes $d$ is actually meant to be $y$.
– axiom111
2 days ago
I have now corrected this.
– axiom111
2 days ago
I have now corrected this.
– axiom111
2 days ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
1
down vote
Subtract second from first you get:
$$15x = 10$$
which means $x = frac23$
So use any equation of the two to find $y$ as
$$y = -95x = -95frac23 = -frac1903$$
answered 2 days ago
Ahmad Bazzi
2,162417
add a comment |Â
up vote
0
down vote
We have $$15x=10$$ or
$$x=frac23.$$
Thus, $$y=-frac95cdot23.$$
answered 2 days ago
Michael Rozenberg
86.9k1576178
add a comment |Â
up vote
0
down vote
Don't rush your steps.
When you solve for $x$, you have:
$$110x = 10 - y$$
$$Rightarrow x = frac10colorred110 - fracy110$$
$$Rightarrow x = frac111 - fracy110$$
Substituting into $95x + y = 0$ we have:
$$95 left(frac111 - fracy110 right)+y = colorred0$$
$$Rightarrow frac9511 - frac95110y + y = 0$$
$$Rightarrow frac9511 - frac95110y + frac110110y = 0$$
$$Rightarrow - frac95110y + frac110110y = 0 - frac9511$$
$$Rightarrow frac15110y = -frac9511$$
$$Rightarrow y = -frac9511 cdot frac11015$$
$$= -frac191 cdot frac103$$
$$= -frac1903$$
Now you can substitute $y$ into any of the two equations to find $x$.
Note: Of course, eliminating $y$ from both equations is much simpler.
answered 2 days ago
Toby Mak
2,4301922
1
@Moo I've edited my answer.
– Toby Mak
2 days ago
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Subtract second from first you get:
$$15x = 10$$
which means $x = frac23$
So use any equation of the two to find $y$ as
$$y = -95x = -95frac23 = -frac1903$$
answered 2 days ago
Ahmad Bazzi
2,162417
add a comment |Â
up vote
1
down vote
Subtract second from first you get:
$$15x = 10$$
which means $x = frac23$
So use any equation of the two to find $y$ as
$$y = -95x = -95frac23 = -frac1903$$
answered 2 days ago
Ahmad Bazzi
2,162417
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Subtract second from first you get:
$$15x = 10$$
which means $x = frac23$
So use any equation of the two to find $y$ as
$$y = -95x = -95frac23 = -frac1903$$
answered 2 days ago
Ahmad Bazzi
2,162417
Subtract second from first you get:
$$15x = 10$$
which means $x = frac23$
So use any equation of the two to find $y$ as
$$y = -95x = -95frac23 = -frac1903$$
answered 2 days ago
Ahmad Bazzi
2,162417
answered 2 days ago
Ahmad Bazzi
2,162417
answered 2 days ago
Ahmad Bazzi
2,162417
answered 2 days ago
Ahmad Bazzi
2,162417
2,162417
add a comment |Â
add a comment |Â
up vote
0
down vote
We have $$15x=10$$ or
$$x=frac23.$$
Thus, $$y=-frac95cdot23.$$
answered 2 days ago
Michael Rozenberg
86.9k1576178
add a comment |Â
up vote
0
down vote
We have $$15x=10$$ or
$$x=frac23.$$
Thus, $$y=-frac95cdot23.$$
answered 2 days ago
Michael Rozenberg
86.9k1576178
add a comment |Â
up vote
0
down vote
up vote
0
down vote
We have $$15x=10$$ or
$$x=frac23.$$
Thus, $$y=-frac95cdot23.$$
answered 2 days ago
Michael Rozenberg
86.9k1576178
We have $$15x=10$$ or
$$x=frac23.$$
Thus, $$y=-frac95cdot23.$$
answered 2 days ago
Michael Rozenberg
86.9k1576178
answered 2 days ago
Michael Rozenberg
86.9k1576178
answered 2 days ago
Michael Rozenberg
86.9k1576178
answered 2 days ago
Michael Rozenberg
86.9k1576178
86.9k1576178
add a comment |Â
add a comment |Â
up vote
0
down vote
Don't rush your steps.
When you solve for $x$, you have:
$$110x = 10 - y$$
$$Rightarrow x = frac10colorred110 - fracy110$$
$$Rightarrow x = frac111 - fracy110$$
Substituting into $95x + y = 0$ we have:
$$95 left(frac111 - fracy110 right)+y = colorred0$$
$$Rightarrow frac9511 - frac95110y + y = 0$$
$$Rightarrow frac9511 - frac95110y + frac110110y = 0$$
$$Rightarrow - frac95110y + frac110110y = 0 - frac9511$$
$$Rightarrow frac15110y = -frac9511$$
$$Rightarrow y = -frac9511 cdot frac11015$$
$$= -frac191 cdot frac103$$
$$= -frac1903$$
Now you can substitute $y$ into any of the two equations to find $x$.
Note: Of course, eliminating $y$ from both equations is much simpler.
answered 2 days ago
Toby Mak
2,4301922
1
@Moo I've edited my answer.
– Toby Mak
2 days ago
add a comment |Â
up vote
0
down vote
Don't rush your steps.
When you solve for $x$, you have:
$$110x = 10 - y$$
$$Rightarrow x = frac10colorred110 - fracy110$$
$$Rightarrow x = frac111 - fracy110$$
Substituting into $95x + y = 0$ we have:
$$95 left(frac111 - fracy110 right)+y = colorred0$$
$$Rightarrow frac9511 - frac95110y + y = 0$$
$$Rightarrow frac9511 - frac95110y + frac110110y = 0$$
$$Rightarrow - frac95110y + frac110110y = 0 - frac9511$$
$$Rightarrow frac15110y = -frac9511$$
$$Rightarrow y = -frac9511 cdot frac11015$$
$$= -frac191 cdot frac103$$
$$= -frac1903$$
Now you can substitute $y$ into any of the two equations to find $x$.
Note: Of course, eliminating $y$ from both equations is much simpler.
answered 2 days ago
Toby Mak
2,4301922
1
@Moo I've edited my answer.
– Toby Mak
2 days ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Don't rush your steps.
When you solve for $x$, you have:
$$110x = 10 - y$$
$$Rightarrow x = frac10colorred110 - fracy110$$
$$Rightarrow x = frac111 - fracy110$$
Substituting into $95x + y = 0$ we have:
$$95 left(frac111 - fracy110 right)+y = colorred0$$
$$Rightarrow frac9511 - frac95110y + y = 0$$
$$Rightarrow frac9511 - frac95110y + frac110110y = 0$$
$$Rightarrow - frac95110y + frac110110y = 0 - frac9511$$
$$Rightarrow frac15110y = -frac9511$$
$$Rightarrow y = -frac9511 cdot frac11015$$
$$= -frac191 cdot frac103$$
$$= -frac1903$$
Now you can substitute $y$ into any of the two equations to find $x$.
Note: Of course, eliminating $y$ from both equations is much simpler.
answered 2 days ago
Toby Mak
2,4301922
Don't rush your steps.
When you solve for $x$, you have:
$$110x = 10 - y$$
$$Rightarrow x = frac10colorred110 - fracy110$$
$$Rightarrow x = frac111 - fracy110$$
Substituting into $95x + y = 0$ we have:
$$95 left(frac111 - fracy110 right)+y = colorred0$$
$$Rightarrow frac9511 - frac95110y + y = 0$$
$$Rightarrow frac9511 - frac95110y + frac110110y = 0$$
$$Rightarrow - frac95110y + frac110110y = 0 - frac9511$$
$$Rightarrow frac15110y = -frac9511$$
$$Rightarrow y = -frac9511 cdot frac11015$$
$$= -frac191 cdot frac103$$
$$= -frac1903$$
Now you can substitute $y$ into any of the two equations to find $x$.
Note: Of course, eliminating $y$ from both equations is much simpler.
answered 2 days ago
Toby Mak
2,4301922
edited 2 days ago
answered 2 days ago
Toby Mak
2,4301922
answered 2 days ago
Toby Mak
2,4301922
answered 2 days ago
Toby Mak
2,4301922
2,4301922
1
@Moo I've edited my answer.
– Toby Mak
2 days ago
add a comment |Â
1
@Moo I've edited my answer.
– Toby Mak
2 days ago
1
1
@Moo I've edited my answer.
– Toby Mak
2 days ago
@Moo I've edited my answer.
– Toby Mak
2 days ago
add a comment |Â
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What is $d$? Is that $y$?
– Dave
2 days ago
Sorry, yes $d$ is actually meant to be $y$.
– axiom111
2 days ago
I have now corrected this.
– axiom111
2 days ago