Question

How many solutions does the system have?

Answer 1

Answer: a

Infinitely many

Step-by-step explanation:

Solve by substitution:

1) Solve $y=2x+1$ for $y$:

$y=2x+1$

2) Substitute $2x+1$ for $y$ in $-4x+2y=2$:

$-4x+2y=2$

$-4x+2(2x-1)=2$

3) Simplify both sides of the equation:

$2=2$

4) Add -2 to both sides of the equation:

$2+-2=2+-2$

5) Simplify both sides of the equation:

$0=0$

Therefore, there are infinitely many solutions.

Solve by elimination:

You cannot solve this system by elimination

Solve by graphing:

The $2$ equations are on top of each other, therefore, the system of equations has infinitely many solutions.