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

What is the solution to this system of equations?

If one solution, write your answer as (#,#) with no spaces.

If no solutions, write none, all lowercase.

If infinitely many solutions, write many, all lowercase.

(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

What is the solution to this system of equations?

If one solution, write your answer as (#,#) with no spaces.

If no solutions, write none, all lowercase.

If infinitely many solutions, write many, all lowercase.

(-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

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.

How much will Brianna pay when the two rental companies cost the same?

Do not use the graph to solve, it is tough to read, so use elimination.

Write your answer as a number with no spaces and no dollar signs.

$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.