Algebra 1 Substitution

Question

Use substitution to solve the system of equations. Type your answer in coordinate format: (x,y)

2x+6y=56

4x+12y=24

Answer 1

Problem:

Algebra 1 Substitution

Use substitution to solve the system of equations. Type your answer in coordinate format: (x,y)

2x+6y=56

4x+12y=24

Solution:

2x + 6y = 56

4x + 12y = 24

First, let's divide by 2 and 4 respectively to reduce both equations to:

x + 3y = 28

x + 3y = 6

How can 28 = 6 ??

This system does not intersect (is parallel), so no solution.

THEREFORE:

No values of (x, y) will satisfy both equations

Answer 2

If you solve the 1st equation for x you get 2x = 56 - 6y

divide both sides by 2 to get x = 28 - 3y

Substitute this into the 2nd equation to get 4(28 - 3y) + 12y = 24

Simplifying to get 112 - 12y + 12y = 24

The 12y's cancel out so you get 112 = 24

This is a false statement so there is no solution.

The lines are actually parallel so they will never cross. Therefore there is no solution.