Question 1

Solve by the substitution method.
-x + 2y = -3 
8x + 3y = -24
A)(-2, -3)
B)(3, -1)
C)(-3, 0)
D)No solution

Accepted Answer

The answer of Solve by the substitution method.
-x + 2y...

Question 2

Solve by the substitution method.
-x + 7y = 47 
8x + 6y = 26
A)(-3, 8)
B)(-2, 7)
C)(2, 8)
D)No solution

Accepted Answer

The answer of Solve by the substitution method.
-x + 7y...

Question 3

Solve using the elimination method.
-- x + 4y = + 2 
-3x - 4y = -26
A)(-2, 6)
B)No solution
C)(7, 1)
D)(6, 2)

Accepted Answer

The answer of Solve using the elimination method.
-- x +...

Question 4

Solve the problem.
-The perimeter of a triangle is 52 cm. The triangle is isosceles now, but if its base were lengthened by 3 cm and each leg were shortened by 2 cm, it would be equilateral. Find the base of the original triangle.
A)17 cm
B)13 cm
C)19 cm
D)14 cm

Accepted Answer

The answer of Solve the problem.
-The perimeter of a triangle...

Question 5

Solve the problem.
-The perimeter of a rectangle is 54 m. If the width were doubled and the length were increased by 15 m, the perimeter would be 98 m. What are the length and width of the rectangle?
A)width 8 m, length 13 m
B)width 7 m, length 20 m
C)width 13 m, length 13 m
D)width 20 m, length 7 m

Accepted Answer

The original perimeter equation is 2(l + w) = 54, leading to l + w = 27. The modified perimeter equation is 2(2w + l + 15) = 98, leading to 2w + l + 15 = 49. Solving these equations gives width = 7 m and length = 20 m.

Question 6

Solve the problem.
-The sum of two numbers is 39 and their difference is 17. Find the numbers.
A)13 and 30
B)26 and 13
C)28 and 11
D)23 and 16

Accepted Answer

The answer of Solve the problem.
-The sum of two numbers...

Question 7

Solve by the substitution method.
-x + y = -2 
x + y = -7
A)No solution
B)(0, -9)
C)(0, 0)
D)(-2, -7)

Accepted Answer

The two equations are parallel lines, meaning they never intersect, so there is no solution.

Question 8

Solve using the elimination method.
-2 x - y = 9 
5x + y = 33
A)(3, 6)
B)(6, 4)
C)(6, 3)
D)No solution

Accepted Answer

Adding the two equations eliminates y: (2x - y) + (5x + y) = 9 + 33, resulting in 7x = 42, so x = 6. Substituting x = 6 into 2x - y = 9 gives 12 - y = 9, so y = 3. Thus, the solution is (6, 3).

Question 9

Solve the problem.
-The sum of two angles is 211°. One angle is 29° less than twice the other. Find the angles.
A)127° and 84°
B)78° and 127°
C)80° and 131°
D)78° and 133°

Accepted Answer

The answer of Solve the problem.
-The sum of two angles...

Question 10

Solve by the substitution method.
-x + y = 6 
5x + 5y = 30
A)(0, 0)
B)(6, 5)
C)Infinite number of solutions
D)(3, 3)

Accepted Answer

The two equations are essentially the same, as the second equation is just the first equation multiplied by 5. This means every solution to the first equation is also a solution to the second, indicating an infinite number of solutions.

Question 11

Solve the problem.
-Two angles have a sum of 96°. Their difference is 22°. Find the angles.
A)39° and 61°
B)75° and 21°
C)57° and 39°
D)59° and 37°

Accepted Answer

The answer of Solve the problem.
-Two angles have a sum...

Question 12

Solve by the substitution method.
-7x + 6y = 55
 -5x - 4y = -39
A)(6, 2)
B)(7, 1)
C)(7, 2)
D)No solution

Accepted Answer

The answer of Solve by the substitution method.
-7x + 6y...

Question 13

Solve by the substitution method.
-x - 4y = 20 
4x - 3y = 15
A)(1, -6)
B)(5, 0)
C)(0, -5)
D)No solution

Accepted Answer

The answer of Solve by the substitution method.
-x - 4y...

Question 14

Solve by the substitution method.
-7x - 5y = 20 
-3x + 3y = -12
A)(0, -4)
B)(0, -3)
C)(-1, -3)
D)No solution

Accepted Answer

Solving the first equation for x gives x = (20 + 5y) / 7. Substituting this into the second equation gives -3((20 + 5y) / 7) + 3y = -12. Solving this equation for y gives y = -4. Substituting y = -4 into the first equation and solving for x gives x = 0. Therefore, the solution is (0, -4).

Question 15

Solve by the substitution method.
-6x + 30 = 6y 
3x - 4y = -16
A)(-4, 1)
B)(-4, 2)
C)(-5, 2)
D)No solution

Accepted Answer

From the first equation, we can express y in terms of x: 6x + 30 = 6y => y = x + 5. Substituting y = x + 5 into the second equation gives 3x - 4(x + 5) = -16, which simplifies to 3x - 4x - 20 = -16, leading to -x = 4, or x = -4. Substituting x = -4 into y = x + 5 gives y = 1. Therefore, the solution is (-4, 1).

Question 16

Solve using the substitution method.
-x = 4 + -4y 
x + 4y = 7
A)Infinitely many solutions
B)No solution
C)(- 1, 8)
D)(- 1, - 8)

Accepted Answer

The answer of Solve using the substitution method.
-x = 4...

Question 17

Solve the problem.
-Find two numbers whose sum is 35 and whose difference is 5.
A)31 and 4
B)15 and 20
C)22 and 27
D)13 and 22

Accepted Answer

The correct numbers are 15 and 20 because 15 + 20 = 35 and 20 - 15 = 5, which satisfies both conditions of the problem.

Question 18

Solve the problem.
-The perimeter of a rectangle is 44 cm. One side is 10 cm longer than the other side. Find the lengths of the sides.
A)6 cm, 10 cm
B)12 cm, 22 cm
C)9 cm, 19 cm
D)6 cm, 16 cm

Accepted Answer

The perimeter of a rectangle is given by the formula 2(length + width). Let x be the length of one side. The other side is x + 10 cm. The equation for the perimeter is 2(x + x + 10) = 44. Simplifying gives 4x + 20 = 44, so 4x = 24, and x = 6. Therefore, the sides are 6 cm and 16 cm.

Question 19

Solve by the substitution method.
--7x + 8y = 42 
2x + 6y = -12
A)(-6, 1)
B)No solution
C)(-6, 0)
D)(-7, 1)

Accepted Answer

The answer of Solve by the substitution method.
--7x + 8y...

Question 20

Solve using the elimination method.
-x + y = -13 
x - y = -1
A)(-7, -6)
B)(-8, -5)
C)No solution
D)(7, -5)

Accepted Answer

Adding the two equations eliminates y, leading to 2x = -14, so x = -7. Substituting x = -7 into the first equation gives y = -6.

Quiz 8: Systems of Equations

Solve by the substitution method. -x + 2y = -3 8x + 3y = -24

Solve by the substitution method. -x + 7y = 47 8x + 6y = 26

Solve using the elimination method. -- x + 4y = + 2 -3x - 4y = -26

Solve the problem. -The perimeter of a triangle is 52 cm. The triangle is isosceles now, but if its base were lengthened by 3 cm and each leg were shortened by 2 cm, it would be equilateral. Find the base of the original triangle.

Solve the problem. -The perimeter of a rectangle is 54 m. If the width were doubled and the length were increased by 15 m, the perimeter would be 98 m. What are the length and width of the rectangle?

Solve the problem. -The sum of two numbers is 39 and their difference is 17. Find the numbers.

Solve by the substitution method. -x + y = -2 x + y = -7

Solve using the elimination method. -2 x - y = 9 5x + y = 33

Solve the problem. -The sum of two angles is 211°. One angle is 29° less than twice the other. Find the angles.

Solve by the substitution method. -x + y = 6 5x + 5y = 30

Solve the problem. -Two angles have a sum of 96°. Their difference is 22°. Find the angles.

Solve by the substitution method. -7x + 6y = 55 -5x - 4y = -39

Solve by the substitution method. -x - 4y = 20 4x - 3y = 15

Solve by the substitution method. -7x - 5y = 20 -3x + 3y = -12

Solve by the substitution method. -6x + 30 = 6y 3x - 4y = -16

Solve using the substitution method. -x = 4 + -4y x + 4y = 7

Solve the problem. -Find two numbers whose sum is 35 and whose difference is 5.

Solve the problem. -The perimeter of a rectangle is 44 cm. One side is 10 cm longer than the other side. Find the lengths of the sides.

Solve by the substitution method. --7x + 8y = 42 2x + 6y = -12

Solve using the elimination method. -x + y = -13 x - y = -1