Question

Solve the system of equations using substitution.

y = −2x + 1
4x + 2y = −3

Infinitely many solutions
No solution
(0, −5)
(−5, 0)

Answer 1

4x+2(-2x+1)=-3
4x-4x+2=-3
2=-3 is not a true statement.

The answer is no solution

Answer 2

The system of equations has no solution

Explanation:

The method of substitution consists in solving one equation for a variable and replacing it in the other equation.

In this case one of the equations is already solved for one of the variables (
`y`):

`y = -2x + 1`

So the next step is to plug this in the other equation wich is:

`4x + 2y = -3`

So we will have

`4x + 2(-2x + 1) = -3`

solving the parenthesis:

`4x-4x -2= -3`

`-2= -3`

wich is not a valid answer, so the system of equations has no solution.