Use substitution to solve the system of equations.
2x-6y=8
-4x+12y=-16
A. (0, -4/3)
B. (4/3,0)
C. (4,0)
D. infinitely many solutions

Question

Use substitution to solve the system of equations.
2x-6y=8
-4x+12y=-16
A. (0, -4/3)
B. (4/3,0)
C. (4,0)
D. infinitely many solutions

igreen · Answer

Substitution goes like this:

Rearrange the first equation so that it equals $x$.

2x - 6y = 8

Add 6y to both sides:

2x = 6y + 8

Divide 2 to both sides:

x = 3y + 4

igreen · Answer

Since $x$ is $3y + 4$, we can input $3y + 4$ in the second equation.

igreen · Answer

$-4x+12y=-16$
$-4(3y + 4)+12y=-16$

Solve for $y$:

$-12y - 16 + 12y = -16$

Add 16 to both sides:

$-12y + 12y = 0$

$0 = 0$

Well, from here you can already tell that it has infinitely many solutions :)

igreen · Answer

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