Solving Linear Equations Using Elimination/Substitution

What type of lines have one solution to a system of equations?

• parallel lines

• intersecting lines

• coinciding lines

• one line

Two linear equations are given below. Exactly how many solutions does this system of equations have?

x - 4y = -20

x - 4y = -8

• one solution

• no solution

• infinite solutions

• two solutions

Solve the following 6 problems using substitution:

3x + 5y = 10

x = y + 6

• ( 5, -1 )

• ( 4, -1 )

• ( 3, 2 )

• ( -1, 5 )

Solve using substitution:

4x - 6y = 20

y = -6x

• ( 1, 4 )

• ( - 0.5, -4 )

• ( 0.35, -2 )

• ( 0.5, -3 )

Solve the system of Equation using elimination:

–x – 7y = 9

–x + 9y = –23

• ( -1, 3 )

• ( 1, -3 )

• ( 5, -2)

• ( 2, 3 )

Solve the system by elimination.

−4x − 4y = 0

4x + 4y = 0

• ( -4, 4 )

• No Solution

• Infinite solutions

• ( 4, -8 )

Solve the system by elimination.

x + 6y = 17

x - 3y = 8

• ( 5, 2 )

• ( 11, 1 )

• No solution

• ( 1, 11 )

Solve using substitution:

-5x -8y = -29

y= 3x

• ( 9, 7 )

• ( 2, 3 )

• ( -1, -3 )

• ( 1, 3 )

Lesly graphed two lines in order to find the solution to a given system of equations.

What is the solution?

• ( -3, -8 )

• ( 3, 8 )

• ( -3, 8 )

• ( 8, 3 )

When you graph the exact same equation twice....

• you will have no solution.

• you will have one solution.

• you will have infinitely many solutions.

• you will graph a giraffe.