Unit 4: Systems of Linear Equations &Inequalities

Unit 4 Learning Targets

LT 4-1: I can solve a system of equations by graphing.

LT 4-2: I can solve a system of equations with Substitution.

LT 4-3: I can solve a system of equations with Elimination.

LT 4-4: I can graph a linear inequality.

LT 4-5: I can solve a system of inequalities with graphing.

LT 4-1: Solving Systems of Equations by Graphing

The intersection of the graphs of a pair of linear equations is used to estimate the solution to the system. If two lines intersect at a point, there is exactly one solution. If two lines are the same, there are infinitely many solutions. If two lines are parallel, there is no solution.

Help Videos:

●       How Do You Solve a System of Equations by Graphing?

●       How Do You Show That a System of Equations Has No Solution?

Practice:

4-1 Math XL

LT 4-2: Solving Systems of Equations by Substitution

Substitution is one method for solving systems of equations. The process involves solving one equation for a variable and substituting the solution into the system’s other equation. This results in an equation in one variable. Solve for the variable and substitute its value into one of the original equations that is in the system to find the value of the second variable.

Help Videos:

●       What Is Another Way of Solving a System of Equations Using the Substitution Method?

●       What's an Example of a Word Problem That Has a System of Linear Equations with Infinite Solutions?

Practice:

4-2 Math XL

LT 4-3: Solving Systems of Equations by Elimination

Elimination is an alternate method for solving systems of equations when it is not easy to use substitution. Multiply one or both equations by a constant to get like coefficients that are opposite to use elimination.

Help Videos:

●       How Do You Solve a System of Equations Using the Elimination by Addition Method?

●       How Do You Solve a System of Equations Using the Elimination by Multiplication Method?

Practice:

4-3 Math XL

LT 4-4: Linear Inequalities in Two Variables

The graph of a linear inequality in two variables shows the solutions of the inequality as a half-plane above or below the boundary line. The boundary line is included in the solution when the inequality symbol is ≤ or ≥ and excluded when the inequality symbol is < or >.

Help Videos:

●       How Do You Graph a Greater Than Inequality on the Coordinate Plane?

●       How Do You Solve and Graph Inequalities from a Word Problem?

Practice:

4-4 Math XL

LT 4-5: Systems of Linear Inequalities

Systems of linear inequalities can be solved by graphing. The solution of a system of inequalities is the intersection of the corresponding half-planes, excluding the boundary lines in the case of a strict inequality.

Help Videos:

●       How Do You Solve a System of Inequalities by Graphing?

●       How Do You Write a System of Inequalities from a Graph?

Practice:

4-5 Math XL

Unit 4 Vocabulary

●       linear inequality in two variables

●       solution of an inequality in two variables

●       solution of a system of linear inequalities

●       system of linear inequalities