Use the Elimination Method to Solve for x and y

2x – y = -2

x + y = 5

adding the equations

... to eliminate y

3x = 3

solve for x, then substitute back to find y

To solve for x and y using the elimination method, follow these steps:

Step 1: Start with the given system of equations:
2x - y = -2 (Equation 1)
x + y = 5 (Equation 2)

Step 2: Multiply both sides of Equation 2 by 2 to create equal coefficients for y:
2(x + y) = 2(5)
2x + 2y = 10 (Equation 3)

Step 3: Add Equation 1 and Equation 3 together to eliminate y:
(2x - y) + (2x + 2y) = -2 + 10
2x + 2x - y + 2y = 8
4x + y = 8 (Equation 4)

Step 4: Rewrite Equation 2 and Equation 4 as a new system of equations:
4x + y = 8 (Equation 4)
x + y = 5 (Equation 2)

Step 5: Subtract Equation 2 from Equation 4 to eliminate y:
(4x + y) - (x + y) = 8 - 5
4x + y - x - y = 3x = 3
3x = 3

Step 6: Solve for x by dividing both sides of the equation by 3:
x = 3/3
x = 1

Step 7: Substitute the value of x (1) into Equation 2 to solve for y:
1 + y = 5
y = 5 - 1
y = 4

Therefore, the solutions are x = 1 and y = 4.