How do you solve this system of equations: $- \frac{3}{5} x + \frac{1}{2} y = - 2 and - x + y = - 3$ $-\frac { 3} { 5} x + \frac { 1} { 2} y = - 2 and - x + y = - 3$ ?

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Answer 1 · 2017-11-26T20:26:08

$x=5\quad,\quad y=2$

We’ll use elimination for this one to cancel out the $y$ terms, in order to first solve for $x$ .

We’ll multiply the first equation by $-2$ :

$-\frac{3}{5}x+\frac{1}{2}y=-2$

$\rightarrow -2(-\frac{3}{5}x+\frac{1}{2}y)=(-2)-2$

$\rightarrow \frac{6}{5}x-y=4$

Now we can add this equation to the other equation to solve for $x$ :

$(\frac{6}{5}x-y=4)\quad +\quad (-x+y=-3)$

$\rightarrow \frac{1}{5}x=1$

$x=5$

Now we can plug the value of $x$ into an equation to find the value of $y$ :

$-x+y=-3$

$\rightarrow -5+y=-3$

$\rightarrow y=2$

Having solved for both variables, we can check our work by plugging those values into one of the equations:

$-\frac{3}{5}x+\frac{1}{2}y=-2$

$-\frac{3}{5}(5)+\frac{1}{2}(2)=-2$

$-3+1=-2$

$-2=-2$

So the answer is right.

How do you solve this system of equations: -\frac { 3} { 5} x + \frac { 1} { 2} y = - 2 and - x + y = - 3−35x+12y=−2and−x+y=−3-\frac { 3} { 5} x + \frac { 1} { 2} y = - 2 and - x + y = - 3?