Solving systems w/ elimination

Question

Find each variable and show each step.

2x - 3y + 4z + w = -7

-3x + 4y + 2z + 4w = 3

x - 5y - 4z - 5w = -4

5x - 2y + 3z + 3w = -17

Answer 1

Elimination Method

For each of the following steps, you will start with a pair of equations. multiply one equation by a constant such that a variable can be eliminated by adding or subtracting with the other equation.

From the original 4 equations, select at random 3 different pairs.

For each pair, eliminate a variable using the Elimination Method. You will now have 3 equations with three unknowns.

From the 3, select TWO pairs at random, and repeat the Elimination Method. You will now have 2 equations with 2 unknowns.

Solve the 2 equations---using again the Elimination Method. You will now be able to solve for one of the variables.

Next, select any pair of the earlier 3-variable equations. Replace the "solved" variable with the value from above. This gives you another pair of equations with 2 variables.

Continue the process until you have found all four variables