How do we solve a system of equations by graphing?

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Need some practice?

• Is (x,y) a solution to the system of equations? (IXL)

• Solve a system of equations by graphing (IXL)

• Solve a system of equations by graphing: word problems (IXL)

• Find the number of solutions to a system of equations by graphing (IXL)

• Classify a system of equations by graphing (IXL)

How do we solve a system of equations by substitution?

1. Solve one of the equations for either variable.

2. Substitute the expression from Step 1 into the other equation.

3. Solve the resulting equation.

4. Substitute the solution in Step 3 into one of the original equations to find the other variable.

5. Write the solution as an ordered pair.

Need some practice?

• Solve a system of equations using substitution (IXL)

• Solve a system of equations using substitution: word problems (IXL)

• Classify a system of equations (IXL)

• Solve a system of equations using augmented matrices (IXL)

• Solve a system of equations using augmented matrices: word problems (IXL)

How do we solve a system of equations by elimination?

1. Determine which variable will be eliminated. ...

2. Combine the equations using addition. ...

3. Solve the new equation for the remaining variable.

4. Substitute the value for that variable into one of the original equations and solve.

5. Check your work by graphing or substitution.

Need some practice?

• Solve a system of equations using elimination (IXL)

• Solve a system of equations using elimination: word problems (IXL)

How do we solve and graph

linear inequalities?

1. Isolate y by itself on one-side of the inequality side.

2. Graph like a linear equation using the y-intercept (b) and the slope (m).

3. Use inequality to have solid or dotted line.

4. Shade above or below based on inequality.

Need some practice?

• Does (x, y) satisfy the inequality? (IXL)

• Linear inequalities: solve for y (IXL)

• Graph a two-variable linear inequality (IXL)

• Write linear inequality from a graph (IXL)

• Write two-variable inequalities: word problems (IXL)

How do we solve and graph

systems of linear inequalities?

1. Graph the first inequality.

2. Graph the boundary line.

3. Shade in the side of the boundary line where the inequality is true.

4. On the same grid, graph the second inequality.

5. Graph the boundary line.

6. Shade in the side of that boundary line where the inequality is true.

7. The solution is the region where the shading overlaps.

8. Check by choosing a test point.

Need some practice?

• Is (x, y) a solution to the system of linear inequalities? (IXL)

• Solve systems of linear inequalities by graphing (IXL)