Algebra 1 Chapter 13 Test

Algebra 1 Part 1 Final Exam Review Day 2

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Multiple Choice

Find the x- and y-intercepts of 3x + 4y = 12

• (3,0) and (0,4)

• (4,0) and (0,3)

• (4,3)

Multiple Choice

Find the x- and y-intercepts of the graph

• (-3,0) and (0,-2)

• (-2,0) and (0,-3)

• (-2,-3)

• (-3,-2)

The y-intercept is where the line crosses the y-axis

The x-intercept is where the line crosses the x-axis

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Fill in the Blanks

Any point on the line is a solution to the equation

(3,9) (2,7) (1,5) (0,3) (-1,1) (-2,-1) (-3,-3) and (-4,-5) are all possible solutions because they are on the line

Multiple Select

Check all points that are a solution to the equation x + 4y = 8

• (0,2)

• (2,-4)

• (-4,3)

To be the solution use the x and y in the equation.

If the numbers are equal then it is a solution

If the numbers are not equal then it is not a solution

Open Ended

Graph x=-4

Put a point on -4 on the x-axis. Then draw a line right through the axis

Open Ended

Graph y=2

Put a point on 2 on the x-axis. Then draw a line right through the axis

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Fill in the Blanks

The solution to a system is the point of intersection which is (1,-3).

It is known as a system with one solution

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Fill in the Blanks

A solution is where the lines intersect and since these two (parallel) lines have no intersection...

There is no solution to the system

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Fill in the Blanks

Since the lines overlap and intersect everywhere...

the system has infinite solutions

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Multiple Choice

Is (3,4) a solution to the system of equations below?

2x - y = 2

x + 2y = 11

• Yes

• No

Substitute the x value and y value from the point into BOTH original equation

Solution - it works for both equations

Not a Solution - it works for only one equation instead of both

Multiple Choice

Solve the system using substitution:

x = -3y + 1

4x -3y = -11

• (1,-2)

• (-2,1)

• No solution

• Infinite solutions

Since the 1st equation states that x can also be written as -3y + 1, we replace the x in the 2nd equation with -3y + 1 (shown with the circle and arrow in the picture to the right)

We solve for x by distributing, combining like terms and then using opposite operations to get x alone

Use the number you get for x in an orginal equation to find y. Your answer is written as a point.

Multiple Choice

Solve the system using elimination:

3x + 2y= 9

2x + 6y =6

• (3,0)

• (0,3)

• No solution

• Infinite solutions

First, the numbers you multiply the equations is found by flipping the coefficients of x. Since both are positive, it is necessary for one of the multiplying negative... this will give you opposites

Add the terms together... x will cancel out so solve for y

use the number for y in an original equation to find x

Multiple Choice

Solve the system by graphing:

y = 2x - 7

2x + 4y = 12

• (1,4)

• (4,1)

• No solution

• Infinite solution

y=2x-7 is in y=mx + b form so you begin at -7 on the y-axis and then use the slope of 2/1 to go up 2 and right 1

2x + 4y = 12 can be graphed using the intercepts of x=6 which is (6,0) and y=3 which is (0,3)

OR solve for y and get y = -2/4x + 3 when solving for y and then beginning at -3 and moving down 2 and right 4

The solution is (4,1)

Multiple Choice

Which special case are you getting if solving the system algebraically gives you 0=0?

• Infinite Solutions

• No solution

Multiple Choice

Which special case are you getting if solving the system algebraically gives you 0=9?

• Infinite Solutions

• No solution

Multiple Choice

Which system represents the following situation?

Amy went to the movies and purchased 4 sodas and 2 popcorns for $22. Jose also went to the movies and purchased 6 sodas and 6 popcorns for $48.

• 4s + 2p = 22 and 6s + 6p = 48

• 4s + 6p = 22 and 2s + 6p = 48+

• 4s + 2p = 22 and 4s + 2p = 48

• 10s + 8p = 22 and s + p = 48

Let s=soda and p=popcorns

soda + popcorn = total cost

Amy bought 4 sodas and 2 popcorns for $22

4s + 2p = 22

Jose bought 6 sodas and 6 popcorns for $48

6s + 6p = 48

Multiple Choice

Amy went to the movies and purchased 4 sodas and 2 popcorns for $22. Jose also went to the movies and purchased 6 sodas and 6 popcorns for $48.

Find the prices for the soda and buckets of popcorn

• soda $22 ; popcorn $48

• soda $10 ; popcorn $8

• soda $5 ; popcorn $3

• soda $3 ; popcorn $ 5