Question

Use the following the system of equations to answer the following.

3x – 9y = -13
x – 3y = -7
(a) Use the substitution method to solve. Show all steps.
(b) Clearly state the solution and what it tells us about the two lines in this system.

Answer 1

(a) Using the substitution method to solve the system of equations:

x - 3y = -7 --> x = 3y - 7

Substitute x = 3y - 7 into the first equation:

3(3y - 7) - 9y = -13

Simplify and solve for y:

9y - 21 - 9y = -13

-21 = -13

This is not a true statement, so there is no solution to the system of equations.

(b) Since there is no solution to the system of equations, this tells us that the two lines are parallel and do not intersect. In other words, there is no point that satisfies both equations.

Answer 2

Explanation:

x = 3y - 7

3x - 9y = -13

3(3y - 7) - 9y = -13

9y - 21 - 9y = -13

-21 ≠ -13

b. The lines are parallel. That means no solution.