Answer ( 10, -2 )
Step by step
2x + 5y = 10
3x - 11y = 52
Addition method - this method is also called the elimination method. In this method, we add two terms with the same variable, but opposite coefficients, so that the sum is zero.
First we need to adjust the x value so they can be eliminated
3 (2x + 5y = 10) multiply all terms by 3
-2 ( 3x - 11y = 52) multiply all terms by -2
6x + 15y = 30
-6x + 22y = -104
-————————-
0x + 37y = - 74
Divide both sides by 37 to solve
37/37 y = -74/37
Simplify
y = -2
Now substitute value of y = -2 into equation to solve for x
2x + 5 (-2) = 10
2x -10 = 10
Add 10 to both sides to isolate variable
2x -10 + 10 = 10 + 10
2x = 20
Divide both sides by 2 to solve for x
2/2 x = 20/2
x = 10
To check my work I graphed the equation to prove my solution