Topic 4: Solving Systems Review

Taxi A charges a fee of $5 plus $2 per mile. Taxi B charges a fee of $4 dollars plus $2.5 per mile. At what distance would the taxis cost the same?

• 1 mile

• 2 miles

• 3 miles

• 4 miles

Answer explanation

$y=2x+5$
$y=2.5x+4$

Solve by substitution.

2x+5=2.5x+4

0.5x=1

x=2,

y=2(2)+5

y=9

What is the solution to the system of equations?

18x+5-y=0

y=18x+1

• (3,5)

• (2,0)

• no solution

• infinitely many

Answer explanation

The slopes are the same, which is 18.

The y-intercepts are different.

What is the solution to the system?

• (-1, 3)

• (-3, 1)

• (3, -1)

• (-3, -1)

Tags

CCSS.8.EE.C.8A

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

Tags

CCSS.8.EE.C.8A

Solve the System using Elimination.

x - 5y = 5

3x + y = 31

• (10, -1)

• (9, 4)

• (10, 1)

• (55, 10)

Answer explanation

multiply the 2nd equation by 5.

so you have 15x+5y=155.

Add to eliminate.

x-5y=5

15x+5y=155

16x=160

x=10

replace x with 10 in the 1st equation.

10-5y=5

y=1

Solve the system by substitution.

5x + 4y= −14

y = −7x − 15

• (-2, -1)

• (1, -2)

• (-2, 1)

• (-1, -2)

Answer explanation

replace y with (-7x-15) in the 1st equation.

5x+4(-7x-15)=-14

5x-28x-60=-14

-23x-60=-14

-23x=46

x=-2

y=-7(-2)-15=14-15=-1

Nia sells pizzas. Large pizzas cost $10 each, and small pizza cost $6 each. She sold 10 pizzas for $92. How many of each size pizza did Nia sell?

• 4 small and 8 large

• 2 small and 8 large

• 6 small and 6 large

• 10 small and 2 large

Answer explanation

s+l=10

6s+10l=92

s=2

l=8

Solve by elimination

-6x + 5y = 1

6x + 4y = -10

• (1,-1)

• (0,-1)

• (1,1)

• (-1,-1)

Answer explanation

Add straight down.

9y=-9

y=-1

Substitute -1 for y in the 1st equation

-6x+5(-1)=1

-6x=6

x=-1

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)
• (3,0)
• No solution(parallel lines)
• Infinitely many solutions

Tags

CCSS.8.EE.C.8B