Solve the system of equations.

Question

x = 6y - 3

2x + 7y = 13 (1 point)

Answer 1

To solve the system of equations, we can use the substitution method.

From the first equation, we have x = 6y - 3. We can substitute this expression for x in the second equation.

2(6y - 3) + 7y = 13

12y - 6 + 7y = 13

19y - 6 = 13

Add 6 to both sides:

19y = 19

Divide both sides by 19:

y = 1

Now, substitute this value of y back into the first equation to find x:

x = 6(1) - 3
x = 6 - 3
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 1.

Answer 2

Solve the system of equations. (1 point)

8x - 3y = - 22.

y = 10 + 4x (1 point))

Answer 3

To solve the system of equations, we can use the substitution method.

From the second equation, we have y = 10 + 4x. We can substitute this expression for y in the first equation.

8x - 3(10 + 4x) = -22

8x - 30 - 12x = -22

Combine like terms:

-4x - 30 = -22

Add 30 to both sides:

-4x = 8

Divide both sides by -4:

x = -2

Now, substitute this value of x back into the second equation to find y:

y = 10 + 4(-2)
y = 10 - 8
y = 2

Therefore, the solution to the system of equations is x = -2 and y = 2.

Answer 4

Solve the system of equations.

5x + 2y = 14

x - 6y = 22 (1 point)

Answer 5

To solve the system of equations, we can use the elimination method.

First, let's multiply the second equation by 5 to make the coefficients of x in both equations the same:

5(x - 6y) = 5(22)
5x - 30y = 110

Now, we have the following system of equations:

5x + 2y = 14 (Equation 1)
5x - 30y = 110 (Equation 2)

By subtracting Equation 1 from Equation 2, we can eliminate the x variable:

(5x - 30y) - (5x + 2y) = 110 - 14
5x - 30y - 5x - 2y = 96
-32y = 96

Divide both sides by -32:

y = 96 / -32
y = -3

Now substitute this value of y in Equation 1:

5x + 2(-3) = 14
5x - 6 = 14
5x = 14 + 6
5x = 20

Divide both sides by 5:

x = 20 / 5
x = 4

Therefore, the solution to the system of equations is x = 4 and y = -3.

Answer 6

Solve the system of equations.

- 9x + y = 12

2x + 4y = - 28 (1 point)

Answer 7

To solve the system of equations, we can use the elimination method.

Multiply the first equation by 4 and the second equation by 1 so that the coefficients of y in both equations are the same:

4(-9x + y) = 4(12)
2x + 4y = -28

Now we have the following system of equations:

-36x + 4y = 48 (Equation 1)
2x + 4y = -28 (Equation 2)

By subtracting Equation 2 from Equation 1, we can eliminate the y variable:

(-36x + 4y) - (2x + 4y) = 48 - (-28)
-36x + 4y - 2x - 4y = 48 + 28
-38x = 76

Divide both sides by -38:

x = 76 / -38
x = -2

Now substitute this value of x in Equation 1:

-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6

Therefore, the solution to the system of equations is x = -2 and y = -6.

Answer 8

How many solutions does the system of equations have?

6x + 2y = - 18

3x + y = 24 (1 point)

Answer 9

To determine how many solutions the system of equations has, we can rewrite the second equation as y = 24 - 3x (by subtracting 3x from both sides).

Now, we can compare the coefficients of x and y in both equations:

Equation 1: 6x + 2y = -18
Equation 2: 0x + 1y = 24 - 3x

We can see that the coefficients of x and y in the two equations are not equal, therefore the lines represented by the equations are not parallel.

Since the lines are not parallel, they must intersect at a single point and the system has exactly one solution.

Therefore, the system of equations has one unique solution.