Systems review

Systems review

Methods for solving systems

• Graphing

• Substitution

• Elimination

Solving by graphing

Graphing both lines and find the point of intersection

Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Multiple Choice

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

• Intersecting lines

• Identical line

• Parallel lines

Multiple Choice

What is the solution?

• No solution

• (0, 2)

• (0, -4)

• (3, -3)

Solving by substitution

Solve one equation for one variable, and substitute it into the other equation.

Multiple Choice

What is the first step to solve the system by substitution?

 $_{y=7x}^{y=4x+3}$  

•  $4x+3=7x$  

•  $y=4\left(7x\right)+3$  

•  $y=7\left(4x+3\right)$  

Multiple Choice

What is the first step to solve the system by substitution?

 $_{y=2x}^{3x+4y=-11}$ 

•  $3x+4\left(2x\right)=-11$ 

•  $3\left(2y\right)+4y=-11$ 

•  $y=2\left(3x+4y\right)$ 

•  $3x+4y=2x$  

Multiple Choice

Solve each system of equations.

y = 3x - 11

2x + 3y = 0

• (-2,3)

• (-3,2)

• (3,-2)

• (2,-3)

y = 3x - 11 and 2x + 3y = 0

2x + 3(3x - 11) = 0

2x + 9x - 33 = 0

11x - 33 = 0

11x = 33

x = 3

y = 3(3) - 11

y = 9 - 11

y = -2

(3, -2)

Multiple Choice

Solve the following systems of equations using substitution:

x + y = 3

3y + x = 5

• No solution

• (1, 2)

• (3, 0)

• (2, 1)

x + y = 3 and 3y + x = 5

Solve either equation for x or y. I solved the first equation for x.

x = 3 - y (Plug this into the other equation for x)

3y + (3 - y) = 5

3y + 3 - y = 5

2y + 3 = 5

2y = 2

y = 1

x = 3 - 1

x = 2

Solving by elimination

Line up your equations, make sure you have matching coefficients, then add or subtract to eliminate a variable.

Multiple Choice

4x + 8y = 20

-4x + 2y = -30

Which variable will be eliminated?

• The x

• The y

• The z

• The unknown

Multiple Choice

Which strategy would help you solve the system using elimination?

2x + 3y = 12

5x - y = 13

• Multiply the first equation by 3 and add it to the second equation

• Multiply the second equation by 3 and add it to the first equation

• Multiply the first equation by 5 and subtract it from the second equation

• Multiply the second equation by 2 and subtract it from the first equation.

Multiple Choice

Solve the system using elimination.

2x + 3y = 12

5x - y = 13

• (-3, -2)

• (1.5, 2)

• (3, 0)

• (3, 2)

2x + 3y = 12

5x - y = 13

2x + 3y = 12 ---> 2x + 3y = 12

3(5x - y=13) ---> 15x - 3y = 39

17x = 51 (divide by 17)

x = 3

5(3) - y = 13

15 - y = 13

-y = -2

y = 2 ---> (3, 2)

Any last minute questions?