Solving Systems by Gaussian Elimination

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE

• FALSE

8x + 14y = 4

-6x - 7y = -10

• (4, -2)

• (-2, 4)

• (0, 3)

• (-4, -2)

Your friend rents 10 chairs and 2 tables for $300. Another friend rents 8 chairs and 4 tables for $360. How much does a chair and a table cost? Write a system of equations to solve.

• Chairs $2 Tables $5

• Chairs $50 Tables $20

• Chairs $10 Tables $15

• Chairs $20 Tables $50

Using Gaussian elimination, solve the system of equations: $$ \begin{align*} 2x + 3y - z &= 7 \\ x - 2y + 4z &= -3 \\ -3x + y + 3z &= 4 \end{align*} $$

Solve the linear systems together by using the values of b for two separate systems, then reducing an appropriate augmented matrix to reduced row echelon form. Write your answer as (x1, x2), (x1, x2) form.

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