Question

Solving Systems by Substitution Day 11. 4x+2y=8y=-2x+4Word bank: (5,-2) (5,5) (2,6) NO SOLUTION INFINITE SOLUTIONS (11, 13) (-2,-6) (0,0) (2.-6) (6,2)

Answer 1

We have to solve the system of equations

`\begin{gathered} 4x+2y=8 \\ y=-2x+4 \end{gathered}`

by substitution.

This method requieres to solve one of the equations for one of the variables and then plugging this value in the other equation. Since in this case the second equation is already solve for y, we plug this value in the first equation to get an equation of only the x variable.

`\begin{gathered} 4x+2(-2x+4)=8 \\ 4x-4x+8=8 \\ 8=8 \end{gathered}`

Since this equation is always true, no matter the value of x, the system of equations has an infinite number of solutions.