Solutions to Equations/Inequalities Graphs

Solutions to Equations/Inequalities Graphs

What does it mean to be a "solution"

• A value that makes the sentence true when you plug it into the equation or inequality

• x = 12 : {12}

• x < 12 : {11, 10, 9, 8, 7, etc.}

There is ONLY ONE solution for this equation.

--> x has to be equal to 12 for this sentence to be true

There are MANY solutions for this inequality.

--> x can be 11, 10, 9, 8, 7, 6, 5, etc. but it cannot be 12.

How to find a solution to a linear equation on a graph:

Find a point on the line; this is one of many solutions.

YOUR TURN.

What are some solutions?

• (-3, -2)

• (-1, 1)

• (0, 3)

• (1, 5)

• (3, 9)

• (2, 7)

Multiple Choice

Which of the following is a solution to the equation?

• (1,1)

• (0,0)

• (5,0)

Multiple Choice

Which of the following is a solution to the equation?

• (0,3)

• (0,0)

• (0,2)

Multiple Choice

Which of the following is a solution to the equation?

• (0,3)

• (0,0)

• (-1,0)

Multiple Choice

Which of the following is a solution to the equation?

• (0,0)

• (1,2)

• (0, -1)

Open Ended

Name one solution of the graph.

Open Ended

Name one solution of the graph.

Open Ended

Name one solution of the graph.

How to find a solution to a linear inequality on a graph:

Find a point in the shaded region or anything on the solid boundary line. This is one of many solutions.

YOUR TURN.

What are some solutions?

• ANYWHERE in the shaded region

• (-1, 1)

• (3, 0)

• (1, 2)

• (3, -9)

• anything on the dashed line is not a solution

What are some solutions?

• ANYWHERE in the shaded region

• (-1, 1)

• (-3, 0)

• (-1, -2)

• (-5, -9)

• (0, 2)

Multiple Choice

Which is a solution to the inequality.

• (0,0)

• (0,5)

• (-4, 0)

Multiple Choice

Which is a solution to the inequality.

• (2, 3)

• (0,2)

• (2, -1)

Multiple Choice

Which is a solution to the inequality.

• (1,0)

• (1,4)

• (2, 0)

Multiple Choice

Which is a solution to the inequality.

• (1,2)

• (1,1)

• (-3, 0)

How to find a solution to a SYSTEM of linear equations on a graph:

Find the point of intersection.

YOUR TURN.

What is the only solution?

• (2, 5)

What if they don't intersect?

• NO SOLUTION

Open Ended

Which is the solution to this system of linear equations?

Open Ended

What is the solution to this system of linear equations?

Open Ended

What is the solution to this system of linear equations?

Open Ended

What is the solution to this system of linear equations?

Open Ended

What is the solution to this system of linear equations?

Open Ended

What is the solution to this system of linear equations?