ccss.hsa.rei.c.6.q.a1.sle.17 - How many solutions does this system of equations have? Explain how you know.

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

The system of equations have infinitely many solutions. This is because when we solve these pair of linear equations we get 0 = 0.

Let us see how!

8x - 2y = -4 \rightarrow equation 1

Writing this in the standard from y = mx +b we get

-2y = -8x -4

Dividing this by -2, the equation 1 becomes

y = 4x +2

12x + 6 = 3y \rightarrow equation 2

Writing this in standard form y = mx + b we get

-3y = -12x -6

Dividing this by -3, the equation 2 becomes

y = 4x + 2

Both equations are identical to each other, so when we equate them across each other to solve them we get,

4x + 2 = 4x + 2

\Rightarrow 0 = 0

This means that the system of equations have infinitely many solutions. Graphing such a system of linear equations on the axis gives us only one straight line.