# Solving SySTEMs Of Equations Test

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Philip Benanti
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Quizzes Created: 18 | Total Attempts: 27,224
Questions: 14 | Attempts: 335

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• 1.

• 2.

• 3.

• 4.

• 5.

### Solve the system:5x + 4y = 495x – 4y = 1

• A.

(5,6)

• B.

(6,5)

• C.

(-5,-6)

• D.

(-6,-5)

A. (5,6)
Explanation
The correct answer is (5,6) because when we substitute x=5 and y=6 into the two equations, we get 5(5) + 4(6) = 49 and 5(5) - 4(6) = 1. Therefore, the solution satisfies both equations and is the correct answer.

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• 6.

### Solve the system:5x + y = 10x + 3y = -26

• A.

(-52.25,8.75)

• B.

(4,-10)

• C.

Infinitely many solutions

• D.

No solution

B. (4,-10)
Explanation
The correct answer is (4,-10). This is the solution to the system of equations 5x + y = 10 and x + 3y = -2. By substituting x = 4 and y = -10 into both equations, we can see that both equations are satisfied. Therefore, (4,-10) is the solution to the system.

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• 7.

### Solve the system:3x + 5y = 62x + 5y = 4

• A.

(5,10)

• B.

(1,0)

• C.

(2,0)

• D.

No Solution

C. (2,0)
Explanation
The correct answer is (2,0) because when we substitute x=2 and y=0 into the equations, we get 3(2) + 5(0) = 6 and 2(2) + 5(0) = 4, which satisfies both equations. Therefore, (2,0) is a solution to the system of equations.

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• 8.

### If a + 3b = 13 and a + b = 5, the value of b is

• A.

1

• B.

7

• C.

4.5

• D.

4

D. 4
Explanation
To find the value of b, we can subtract the equation a + b = 5 from the equation a + 3b = 13. This will eliminate the variable a and leave us with 2b = 8. Dividing both sides by 2, we get b = 4. Therefore, the value of b is 4.

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• 9.

### What is true of the graphs of the two lines 2x – 2y = 6 and 2x + 3y = 21?

• A.

No Solution

• B.

Intersect at (3,6)

• C.

Intersect at (6,3)

• D.

Infinitely many solutions

C. Intersect at (6,3)
Explanation
The two lines 2x - 2y = 6 and 2x + 3y = 21 intersect at the point (6,3). This means that the coordinates (x,y) of the point (6,3) satisfy both equations simultaneously, indicating that the lines intersect at this specific point.

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• 10.

### What is true of the graphs of the two lines 2x + 3y = 6 and -6x – 9x = -18?

• A.

No Solution

• B.

Intersect at (-4,-6)

• C.

Intersect at (0,0)

• D.

Infinitely many solutions

D. Infinitely many solutions
Explanation
The given answer, "Infinitely many solutions," is correct because the two equations represent the same line. By simplifying both equations, we can see that they are equivalent: 2x + 3y = 6 simplifies to y = -2/3x + 2, and -6x - 9y = -18 simplifies to y = -2/3x + 2. Since the two equations have the same slope and y-intercept, they represent the same line and therefore have infinitely many solutions.

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• 11.

### What is true of the graphs of the two lines -5x + 5y = -50 and 4x + 3y = 26?

• A.

No Solution

• B.

Intersect at (8,-2)

• C.

Intersect at (-1,8)

• D.

Infinitely many solutions

B. Intersect at (8,-2)
Explanation
The correct answer is "Intersect at (8,-2)". This means that the two lines represented by the equations -5x + 5y = -50 and 4x + 3y = 26 intersect at the point (8,-2). In other words, there is a single point where the two lines meet on the coordinate plane.

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• 12.

### What is the value of the y-coordinate of the solution to the system of equations 2x + y = 8 and x − 3y = −3?

• A.

-2

• B.

2

• C.

3

• D.

-3

B. 2
Explanation
To find the value of the y-coordinate, we need to solve the system of equations. First, we can solve the second equation for x in terms of y: x = 3y - 3. Then, we substitute this expression for x into the first equation: 2(3y - 3) + y = 8. Simplifying this equation gives us 7y - 6 = 8. Solving for y, we find y = 2. Therefore, the value of the y-coordinate of the solution is 2.

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• 13.

### What is the solution of the system of equations  c + 3d = 8 and c = 4d − 6?

• A.

C = −14, d = −2

• B.

C = −2, d = 2

• C.

C = 2, d = 2

• D.

C = 14, d = −2

C. C = 2, d = 2
Explanation
The given system of equations can be solved by substitution. We can substitute the value of c from the second equation into the first equation. By substituting c = 4d - 6 into c + 3d = 8, we get 4d - 6 + 3d = 8. Simplifying this equation, we get 7d - 6 = 8. Solving for d, we find d = 2. Substituting this value of d back into the second equation, we get c = 4(2) - 6 = 2. Therefore, the solution to the system of equations is c = 2, d = 2.

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• 14.

### Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged \$3.30. Briana purchases five doughnuts and two cookies at the same shop for \$4.95. All the doughnuts have the same price and all the cookies have the same price. Find the cost of one doughnut.

• A.

\$0.60

• B.

\$0.75

• C.

\$1.35

• D.

\$1.50

B. \$0.75
Explanation
Let's assume the cost of one doughnut is x and the cost of one cookie is y. According to the given information, we can set up two equations:

2x + 3y = 3.30 (equation 1)
5x + 2y = 4.95 (equation 2)

To solve these equations, we can multiply equation 1 by 5 and equation 2 by 2 to eliminate y:

10x + 15y = 16.50 (equation 3)
10x + 4y = 9.90 (equation 4)

By subtracting equation 4 from equation 3, we get:

11y = 6.60
y = 0.60

Substituting the value of y back into equation 1, we can solve for x:

2x + 3(0.60) = 3.30
2x + 1.80 = 3.30
2x = 1.50
x = 0.75

Therefore, the cost of one doughnut is \$0.75.

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• Current Version
• Mar 21, 2023
Quiz Edited by
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• Dec 18, 2014
Quiz Created by
Philip Benanti

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