Systems of Inequalities

byTammy Wallace

Varina High School

What is a System of Inequality?

A SYSTEM OF EQUATIONS is:

SOLUTIONS to a SYSTEM OF INEQUALITIES are:

two or more linear inequalities with the same variables being compared.

all points within the overlapping shaded region that makes each inequality in system true. The graph of a system shows all of its solutions.

Find 2 possible solutions for each graph. If a solution can be on the line,

make sure 1 of the 3 points are one that line.

(0, 0)

(2, 0)

(1, 1)

(-2, -3)

(-1, 2)

(1, -1)

Find 2 possible solutions for each graph. If a solution can be on the line,

make sure 1 of the 3 points are one that line.

(-2, 5)

(-1, -4)

(-4, 4)

(0, -2)

(1, 8)

(-6, 0)

Using Slope Intercept Form to write the system of inequality for any given graph.

Start with your y-intercept (b), then move to another the slope.

After writing the equation in Slope-Intercept From, replace the equal sign with the appropriate inequality sign.

Dotted Line

Shaded Above

Shaded Below

SolidLine

Given the systems graphed, write the equations for the

systems.

b

(0, 4)

0

y = 4

y < 4

Given the systems graphed, write the equations for the

systems.

b

(0, -1)

m

m

−𝟑𝟒

𝒚=−𝟑𝟒𝒙 −𝟏

𝒚<−𝟑𝟒𝒙−𝟏

Given the systems graphed, write the equations for the

systems.

𝒚<−𝟑𝟒𝒙−𝟏

The system of inequality is equal to:

Which line can a solution to this system be located?Neither line because the lines are dotted.

y < 4

Given the systems graphed, write the equations for the

systems.

b

(0, 0)

1

y = x

y > x

m

m

m

Given the systems graphed, write the equations for the

systems.

b(0, 3)

m

m

−𝟑𝟐

𝒚=−𝟑𝟐𝒙+𝟑

𝒚<−𝟑𝟐𝒙+𝟑

Given the systems graphed, write the equations for the

systems.

𝒚 ≤−𝟑𝟐𝒙+𝟑

The system of inequality is equal to:

What are 3 solutions to the system?

(1, 0)(-3, 2)(-2, -1)

y > x