Solving Systems of Equations by Graphing

Solving Systems of Equations by Graphing

Students will solve systems of linear equations graphically and algebraically.

Systems of Equations Graphically

• A system of equations is two or more equations with the same variables.

• To solve a system of equations with two variables, find the ordered pair that SATISFIES all of the equations.

Multiple Choice

Determine if the solution  $\left(3,\ -1\right)$  satisfies the system  $2x-5y=11$  
 $-3x+4y=-13$  

• yes

• no

Multiple Choice

Does the solution  $\left(2,-3\right)$  satisfy the system  $4x+3y=-17\ \ \ \ \ \ \ \ -7x-2y=20$  

• yes

• no

Types of Solutions

Multiple Choice

How many types of solutions are there?

• One

• Two

• Three

Multiple Choice

Which solution type has the same slope and the graphs are parallel?

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

Which solution type has the same slope and same y-intercept?

• No Solution

• One Solution

• Infinitely Many Solutions

Multiple Choice

Which solution type has it where the graphs intersect at a single point?

• Infinitely Many Solutions

• One Solution

• No Solution