Module 7 Systems of Equations Review

Module 7 Systems of Equations Review

Directions

• Solve each problem.

• If you get it right, you can skip the next slide and continue.

• If you get it wrong, pay attention to the next page.

• This page will have the solution and a short explanation.

Multiple Choice

What is the solution to this system of equations?

• (2, 0)

• (0, 1)

• (-1, 1/2)

• (-1, 3/2)

(-1, 3/2)

For this system, the lines intersect, so there is one solution. They meet 1 to the left and 1.5 up. 1.5 is also 3 halves or 3/2!

Fill in the Blanks

(2, -5)

Since the y-variables are already opposites, just add. you get 12x = 24. Solve for x to get 2 and then plug the 2 into either problem and solve for y ( 8(2) + y = 11) and you will get -5.

Multiple Choice

 Which graph represents the following system of equations? $2x+y=-1$  $y=3x+4$  

(-1, 1)

The first equation needs to be turned into slope-intercept form first by moving the 2x to the right side and becoming y = -2x - 1. Plot your first point at -1 on the y-axis and then move down 2 right 1 or up 2 left 1.

The second equation is already set to graph, y = 3x + 4. Plot your first point at 4 on the y-axis and move up 3 right 1 or down 3 left 1.

Multiple Choice

A store has a certain brand of shorts on sale for x dollars and all T-shirts on sale for y dollars. The system of equations shows the total amount spent by customers during the first hour of the sale on two different days.

How many solutions does the system have?

• One Solution

• Two Solutions

• No Solutions

• Infinitely Many Solutions

No Solutions

Since there are no opposite coefficients, you have to decide on which to eliminate. If you eliminate the x-variables, you need to multiply the top equation by -2 which creates -10x - 6y = -116.

Next is to add the equations and both variables are eliminated. You are left with 0 = 48, which is a FALSE statement....therefore NO solutions work.

Fill in the Blanks

(-1, 3)

You can eliminate the x-variables by changing all the signs of one equation (multiply by -1) or you can eliminate the y-coordinates by multiplying the bottom equation by 3.

Let's eliminate the x-coordinates, change the bottom equation to -2x + y = 5 and ADD the equations. You get 4y = 12, which means y = 3.

Now plug the 3 into either y to solve for x. 2x - 3 = -5 becomes 2x = -2 so that x = -1.

Multiple Select

Ginger earned $250 selling candles. She sold x small candles for $12.50 each and y large candles for $25.00 each.

If Ginger sold a total of 14 candles, how many small and large candles did she sell?

Select 2 answers

• 8 small

• 8 large

• 6 small

• 6 large

8 small and 6 large

Ginger sold 14 candles, so equation 1 is x + y = 14. The second equation was the money she sells them for and how much she made, 12.50x + 25.00y = 250

You can eliminate either variable by multiplying the x + y = 14 by either -12.50 or -25, Let's eliminate the x by multiplying by -12.50 to create -12.50x - 12.50y = -175.

When you add the two equations now you get 12.50y = 75, which means y = 6.

Now plug the 6 into either equation to solve for y. use the x + y = 14, so x + 6 = 14 which means x = 8.

8 small candles (x) and 6 large candles (y)

Multiple Choice

Brianna is comparing the cost of renting a bicycle from two different companies. Option A charges a fixed fee and an hourly rate. Option B charges per hour with no fixed fee. The system of equations shows the total cost, y, for x hours.

Which graph represents this?

Graph 3

This one is tough to graph since the slopes are not counting by 5 or 10.

The first equation, y = 6x + 16, starts at 16 and goes up 6 and right 1.

The second equation, y = 14x, has a yintercept of 0, so you start at the origin and go up 14 right 1.

Fill in the Blanks

$28.00

You can eliminate the y-variables by multiplying by -1 (just change everyone's signs). Remember the y is the total cost, so. thatis what we want!

The top equation becomes -y = -6x - 16. When you add them together you get 0 = 8x -16 but you have to move the -16 over to solve for x, so you get 16 = 8x or x = 2.

Now take the 2 and plug it in to solve for y, y = 14(2) which is y = 28.