Pick one of the two equations and solve for one of the variables first.

So let's say I picked the first one, 3x + 2y = -7 and solved for x.

3x + 2y = -7

3x = -2y - 7

x = -2y/3 - 7/3

Now, plug in the value for x into the second equation in order to solve for y.

5x + 37 = 3y

5(-2y/3 - 7/3) + 37 = 3y

-10y/3 - 35/3 + 37 = 3y

-10y/3 - 35/3 + 37 = 9y/3

-35/3 + 37 = 10y/3 + 9y/3

19y/3 = 111/3 - 35/3

19y/3 = 76/3

19y = 76

y = 4

Now use the value for y for the first equation, where you solved for x.

x = -2y/3 - 7/3

= -2(4)/3 - 7/3

= -8/3 - 7/3

= -15/3

= -5

So now we have values for both x and y.

**x = -5 and y = 4.**

We can also use this to check our answers. Plug these two numbers in to the correct variables for the first equation.

3x + 2y = -7

3(-5) + 2(4) = -7

-15 + 8 = -7

-7 = -7 <---- The first equation works. Now for the second equation.

5x + 37 = 3y

5(-5) + 37 = 3(4)

-25 + 37 = 12

12 = 12 <---- The second equation also works.

Therefore, y = 4 and x = -5 are the correct answers.