Question

Solve the system of equations using elimination: minus, 5, x, plus, 2, y, equals, 1−5x+2y=1 and minus, 4, x, minus, y, equals, 19−4x−y=19. Answer

Answer 1

The solution to the system of equations using elimination method is x = -3 and y = -7. Multiplying the second equation by 2 allowed us to eliminate the variable y by adding the modified equation to the first one, and then solving for x and subsequently y.

Step-by-step explanation:

To solve the system of equations using elimination, we have the following two equations:

• (1) -5x + 2y = 1
• (2) -4x - y = 19

To eliminate one of the variables, we can multiply equation (2) by 2 to get:

• (3) -8x - 2y = 38

Now, add equation (1) and equation (3):

• (1) -5x + 2y = 1
• (3) -8x - 2y = 38
• (4) -13x = 39

Divide both sides of equation (4) by -13 to find x:

• x = -3

Substitute x = -3 into equation (2) to find y:

• -4(-3) - y = 19
• 12 - y = 19
• -y = 19 - 12
• -y = 7
• y = -7

The solution to the system of equations is x = -3 and y = -7.