Question

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

Answer 1

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

Explanation:

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`

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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.