Question

Y=2x+82x-y=-8What is the “y” to satisfy the equation?

Answer 1

A line equation can be written in slope-intercept form, which is:

`y=mx+b`

where m represents the slope and b represents the y-intercept.

The solution of a linear system is given by the intercept of the lines. If the line crosses each other, the system has one solution, if the lines are equal the system has infinite solutions, and if the lines are parallel the system has no solutions.

If we rewrite both our equations in slope-intercept form, we have:

`\begin{cases}y={2x+8} \\ 2x-y={-8}\end{cases}\implies\begin{cases}y={2x+8} \\ y={2x+8}\end{cases}`

Since the equations are equal, those lines are equal, therefore, this system has inifinite solutions. Any y value would satisfy the equations.