Notes: Solving Systems of Linear Inequalities by Graphing

When we graph a ___________ ________________, the _________represents every
solution to that linear equation.

When we graph a linear ________________, the solution is represented by an entire
_____________________ (not just the line). We represent this region by
___________________________.

We graph a _______________ line if the line is included in the solution (___or ___). We
graph a _______________ if the line is not included in the solution (___or ___).

If 𝑦 is ____________________ the expression involving 𝑥, shade _________ the line.
Otherwise, shade _____________ the line.

The ______________________ is where the shaded region is ________________.
Example
𝒚 < 𝟐𝒙 + 𝟓
𝟏
𝒚≥− 𝒙−𝟏
𝟐
Examples (solving systems of inequalities by graphing)
1.
𝑥+𝑦 >2
−4𝑥 + 2𝑦 < 8
2.
3𝑥 − 𝑦 ≥ 2
𝑦 > 3𝑥 + 5
3.
𝑦 ≥ −4
𝑥<8
Application
4.
Philip makes $15 per hour working for a photographer. He also coaches a soccer team for $10 per hour. He
needs to earn at least $90 per week, but is unable to work for more than 20 hours per week.
a)
Write a system of equations to model the situation.
Assign x to the photography job and y to the soccer job.
b)
Solve the inequality for y and graph on the coordinate plane.