Solving Systems of Equations by Elimination (MULTIPLY FIRST)

Question

x - 4y = -1

5x + 2y = 17

Steps for Solving a System of Equations by Multiplying:

1. Decide which variable to eliminate
2. Multiply one or both equations by a constant so that adding or subtracting the equations will eliminate the variable
3. Solve the system of equations

Answer 1

Step 1: Let's eliminate the y variable.

Step 2: To do this, we need to multiply the second equation by 2. This will make it so that equation 1 and +4y and equation 2 to have -4y, which will cancel when solving the system of equations.

2(5x + 2y = 17)

10x + 4y = 34

Step 3: Add equations 1 and 2 and solve for x.

(x - 4y = -1)

+(10x + 4y = 34)

11x = 33

-------------------

11x / 11 = 33 / 11

x = 3

Step 4: Plug in x back into either of the given equations. I'll plug it back into equation 1 as it looks easier to solve, but both equations would work.

3 - 4y = -1

3 - 4y - 3 = -1 - 3

-4y = -4

y = 1