Question

Write the four steps for using the linear combination method to solve a system of equations.

Solve this system using the linear combination method. Show your work.

4x + 2y = 5
−4x − 5y = 7

Answer 1

Explanation:

The four steps of linear combination method are

1) Rearrange like terms such that they are in the same column.

2) The next step is to decide on which variable you want to eliminate and multiply each row with suitable numbers that would make the coefficient of the variable to be equal and opposite.

3) Add both rows and solve for the other unknown variable.

4) substitute the known variable into any of the equations and solve for the other variable.

4x + 2y = 5

−4x − 5y = 7

We would eliminate x by adding both equations. It becomes

- 3y = 12

y = 12/- 3 = - 4

Substituting y = - 4 into the first equation, it becomes

4x + 2 × - 4 = 5

4x - 8 = 5

4x = 5 + 8 = 13

x = 13/4 = 3.25