Question

Solve, using the substitution method.

y + 2x = 7
14 – 4x = 2y

A. The solution is (1, 5)

B. The solution is (21, 0)

C. There are an infinite number of solutions.

D. There is no solution.

Answer 1

y+2x=7

14-4x=2y

Solve 2x+y=7 for y

Add -2x to both sides

2x+y+-2x=7+-2x

y=-2x+7

Substitute -2x+7 for in -4x+14=2y

-4x=14=2y

-4x+14=2(-2x+7)

Simplify both sides of the equation

-4x+14=-4x+14

Add 4x to both sides

-4x+14+4x=-4x+14+4x

14=14

Add -14 to both sides

14+-14=14+-14

0=0

Infinitely many solutions

Answer : C

Answer 2

14-4x=2y
divide both sides by 2
7-2x=y
subsitute 7-2x for y
7-2x+2x=7
add like terms
7=7
true
therefor these 2 equations are the same and there are an infinite number of equations


answer is C