Find the solution of the system of equations.5, x, plus, 10, y, equals, minus, 55x+10y=−5minus, 5, x, minus, y, equals, 32−5x−y=32

The system of equations is:

5x + 10y = -55 -5x - y = 32

Let's solve it step by step:

Step 1: Simplify the equations if possible. The first equation can be simplified by dividing all terms by 5:

x + 2y = -11

So now we have:

x + 2y = -11 -5x - y = 32

Step 2: It's easier to solve the system if one of the equations has only one variable. We can achieve this by adding the two equations together:

(x + 2y) + (-5x - y) = -11 + 32 -4x + y = 21

Step 3: Now we can solve this equation for y:

y = 4x + 21

Step 4: Substitute y in the first equation:

x + 2(4x + 21) = -11 x + 8x + 42 = -11 9x = -53 x = -53 / 9 x = -59/9

Step 5: Substitute x = -59/9 in the equation y = 4x + 21 to find y:

y = 4(-59/9) + 21 y = -236/9 + 189/9 y = -47/9

So the solution of the system is x = -59/9, y = -47/9.