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

Solving by Substitution

Steps 1 & 2

Solving by Substitution

Steps 3 & 4

The solution is (42,-12)

Solving by Substitution

Example 2

Fill in the Blank

Solve this system of equations for x.

-3x + 4y = 29

y = 2x + 11

Multiple Choice

Solve this system of equations for y.

-3x + 4y = 29

y = 2x + 11

• y = 2

• y = 4

• y = 5

• y = 6

Multiple Choice

Use Substitution to solve the system:

x = 2y - 9

2x + 3y = 17

• (1,2)

• (1,5)

• (5,1)

• (2,1)

Multiple Choice

Use Substitution to solve the system

3y-8 = x

3x - 4y = -9

• (1,3)

• (3,1)

• (2,5)

• (1,5)

Solving by Elimination

Steps 1 & 2

Solving by Elimination

Steps 3/4 & 5/6

The solution is (2,4)

Solving by Elimination

Example 2

Multiple Choice

Solve the system of equations
  4x+8y=20
-4x+2y=-30

• (-7,1)

• (2,-5)

• (-2,5)

• (7,-1)

Multiple Choice

Where do these lines intersect?
x-y=11
2x+y=19

• (10,-1)

• (-1,10)

• (3,-4)

• (6,7)

Multiple Choice

Solve the system using elimination.
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Fill in the Blank

Use elimination to solve the system of equations

$$2x\ +\ 3y\ =\ 6$$  

$$x\ +\ 2y\ =\ 5$$  

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-

,

)