Question

Solve using the elimination method.

[7x + 6y = 19]
[x - 12y = 16]

Answer 1

Using the elimination method to solve the system of equations, we find that x = 49/5 and y = -31/30. These values satisfy both of the original equations when checked.

Step-by-step explanation:

The question involves solving a system of equations using the elimination method. We are given two linear equations:

1. 7x + 6y = 19
2. x - 12y = 16

To use the elimination method, we need to manipulate these equations so that we can cancel one variable by adding or subtracting the equations. Let's multiply the second equation by 7 so we can eliminate the x variable:

1. 7x + 6y = 19 (Equation 1)
2. 7(x - 12y) = 7(16)

Expanding the second equation after multiplication, we get:

1. 7x + 6y = 19
2. 7x - 84y = 112

Now, subtract Equation 1 from the modified second equation:

• (7x + 6y) - (7x - 84y) = 19 - 112
• 7x - 7x + 90y = -93
• 90y = -93

Divide by 90 to solve for y:

y = -93/90 = -31/30

Now that we have the value of y, we can substitute it into one of the original equations to find x. We'll use the second equation:

x - 12(-31/30) = 16

x + 31/5 = 16

x = 16 - 31/5

x = (80/5) - (31/5)

x = 49/5

After solving, we find that x = 49/5 and y = -31/30. It's important to check the answer is reasonable by plugging these values back into the original equations.