Step 1: Arrange the equations with like terms in columns
5x + y = 2
4x + y = 5
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Step 2: One set of coefficients shouls be opposites. In our case, we multiply the second equation by - 1
5x + y = 2
-4x - y = - 5 (Multiplied by - 1)
Step 3: We add the like terms
5x + - 4x = 5x - 4x = x
+y + - y = y - y = 0
2 + - 5 = 2 - 5 = -3
Important: please be careful with the negative and positive signs
Step 4: Solve for x
x = - 3
Step 5 : Solve for y in any of the equations, replacing x
5x + y = 2
5 * - 3 + y = 2
-15 + y = 2
y = 2 + 15
y = 17
Step 6: We write the solution as an ordered pair
(-3, 17)