System of Equations Substitution No Graphs

Two or more linear equations with the same variables

• Set of Linear Equations

• System of Linear Equations

• Process of Linear Equations

• Multiple Linear Equations

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are in slope-intercept form.

• Make sure both equations can be solved.

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together

Which is the best method to use?

y = 6x − 11

−2x − 3y = −7

• Graphing

• Substitution because a variable is isolated.

• Elimination because both equations are in standard form.

What variable do you eliminate?

4x + 8y = 20

−4x + 2y = −30

• X because they have opposite signs

• Y because they have opposite signs

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

Solve the system of Equation (x,y)
–x + 9y = –5
x –5y = 1  

• (-4,-1)

• (4,1)

• (-4,1)

• (1,4)