Question

Determine the solution to the system of equations below.

-5x – 7y = 11

x – 2y = -9
Responses
A Infinitely many solutionsInfinitely many solutions
B x = -5, y = 2x = -5, y = 2
C No solutionNo solution
D x = -5, y = -7

Answer 1

6x + 3y = 9
2x + 3y = 1

Solve the system of equations.
Responses
A x = 2, y = -1
B x = -1, y = 2
C x = -1/2, y = 3x = - 1 2 , y = 3
D x = 3, y = -1/2
E x = 1, y = 1

Answer 2

3x + y = 3
x + y = 2

Solve the system of equations.
Responses
A x = 1/2, y = 3
B x = 3, y = 1/2
C x = 1/2, y = 3/2
D x = 3/2, y = 1/2
E x = 5/2, y = -9/2

Answer 3

3x + 19y = 2

19x + 3y = 130


What is the solution for the system of equations above?
Responses
A x = 1, y = -7x = 1, y = -7
B x = -7, y = -1x = -7, y = -1
C x = 7, y = -1x = 7, y = -1
D x = -7, y = 1

Answer 4

2x - 2y = 6
3x + 2y = 9

Solve the system of equations.
Responses
A x = 0, y = 3x = 0, y = 3
B x = 3, y = 0x = 3, y = 0
C x = 1, y = -2x = 1, y = -2
D x = -2, y = 1x = -2, y = 1
E x = 6, y = 3

Answer 5

Use the graphing method to solve the system of linear equations:

y = -x + 3 and y = x - 1
Responses
A (-1,2)(-1,2)
B (0,3)(0,3)
C (1,0)(1,0)
D (1,2)(1,2)
E (2,1)

Answer 6

To determine the solution to the system of equations, we can use the method of substitution or elimination.

Let's start by solving using the method of substitution:

From the second equation, we can express x in terms of y:
x = -9 + 2y

Now substitute this value of x into the first equation:
-5(-9 + 2y) - 7y = 11
45 - 10y - 7y = 11
-17y = -34
y = 2

Substitute this value of y back into the second equation to find x:
x - 2(2) = -9
x - 4 = -9
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 2.
The correct answer is B.

Answer 7

To solve the system of equations, we can use the method of either substitution or elimination. Let's solve by using the method of elimination:

Multiply the second equation by 3 so that the coefficients of y in both equations are the same:
6x + 3y = 9
6x + 9y = 3

Subtract the two equations:
(6x + 3y) - (6x + 9y) = 9 - 3
-6y = 6
y = -1

Substitute this value of y back into either of the original equations. Let's use the first equation:
6x + 3(-1) = 9
6x - 3 = 9
6x = 12
x = 2

Therefore, the solution to the system of equations is x = 2 and y = -1.
The correct answer is A.

Answer 8

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it by using the method of elimination:

Multiply the second equation by -1:
-(x + y) = -2

Distribute the negative sign:
-x - y = -2

Now add the two equations together:
3x + y + (-x - y) = 3 + (-2)
2x = 1
x = 1/2

Substitute this value of x back into either of the original equations. Let's use the second equation:
1/2 + y = 2

Subtract 1/2 from both sides:
y = 2 - 1/2
y = 3/2

Therefore, the solution to the system of equations is x = 1/2 and y = 3/2.
The correct answer is C.

Answer 9

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it by using the method of elimination:

Multiply the first equation by 3 and the second equation by 19 to eliminate the x term:
9x + 57y = 6
361x + 57y = 2470

Subtract the first equation from the second equation:
361x + 57y - (9x + 57y) = 2470 - 6
352x = 2464
x = 2464/352
x = 7

Substitute this value of x back into either of the original equations. Let's use the first equation:
3(7) + 19y = 2
21 + 19y = 2
19y = 2 - 21
19y = -19
y = -19/19
y = -1

Therefore, the solution to the system of equations is x = 7 and y = -1.
The correct answer is C.

Answer 10

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it by using the method of elimination:

Multiply the first equation by 3 and the second equation by 2 to eliminate the y term:
6x - 6y = 18
6x + 4y = 18

Subtract the first equation from the second equation:
6x + 4y - (6x - 6y) = 18 - 18
10y = 0
y = 0

Substitute this value of y back into either of the original equations. Let's use the first equation:
2x - 2(0) = 6
2x = 6
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 0.
The correct answer is B.

Answer 11

To solve the system of linear equations using the graphing method, we can graph both equations on the same coordinate plane and find the point of intersection.

The first equation, y = -x + 3, has a y-intercept of 3 and a slope of -1. We can plot the point (0, 3) and then find another point by moving 1 unit to the right and 1 unit down. Let's plot the point (1, 2).

The second equation, y = x - 1, has a y-intercept of -1 and a slope of 1. We can plot the point (0, -1) and then find another point by moving 1 unit to the right and 1 unit up. Let's plot the point (1, 0).

Now, we can see that the two lines intersect at the point (1, 2).

Therefore, the solution to the system of linear equations is x = 1 and y = 2.
The correct answer is D.