Question

How can the linear combination method be utilized to solve the following system of equations? Explain each step of your solution:

2x - 3y = 13
x + 2y = -4

Answer 1

To solve the system of equations using the linear combination method, multiply the second equation by 2 and subtract the first equation from the second equation to eliminate x. Solve for y and substitute the value of y into one of the original equations to solve for x.

Step-by-step explanation:

To solve the system of equations using the linear combination method, we can multiply both sides of one of the equations by a suitable number to make the coefficients of one of the variables the same in both equations. In this case, we can multiply the second equation by 2 to make the coefficients of y the same. This gives us:

2x - 3y = 13

2x + 4y = -8

Next, we can subtract the first equation from the second equation to eliminate x. This gives us:

2x + 4y - (2x - 3y) = -8 - 13

7y = -21

Dividing both sides of the equation by 7, we find that y = -3.

Substituting this value of y into one of the original equations, we can solve for x. Using the first equation:

2x - 3(-3) = 13

2x + 9 = 13

2x = 4

x = 2