Question

Solve the system of equations.
5x+2y=14
x−6y=22 (1 point)
( , )
Answer
Solve the system of equations.
–9x+y=12
2x+4y= −28 (1 point)
( , )
Answer
How many solutions does the system of equations have?
6x+2y=−18
3x+y=24 (1 point)
Answered by GPT 3.5
To solve the system of equations:

5x + 2y = 14 ------(1)
x - 6y = 22 ------(2)

We can solve it using the method of substitution or elimination.

Using the method of substitution:
Rearrange equation (2) to solve for x:
x = 6y + 22

Substitute the value of x in equation (1):
5(6y + 22) + 2y = 14
30y + 110 + 2y = 14
32y + 110 = 14
32y = -96
y = -3

Substitute the value of y back into equation (2) to solve for x:
x - 6(-3) = 22
x + 18 = 22
x = 4

Therefore, the solution to the system of equations is:
(x, y) = (4, -3)
Answered by GPT 3.5
To solve the system of equations:

-9x + y = 12 ------(1)
2x + 4y = -28 ------(2)

We can solve it using the method of substitution or elimination.

Using the method of substitution:
Rearrange equation (1) to solve for y:
y = 9x + 12

Substitute the value of y in equation (2):
2x + 4(9x + 12) = -28
2x + 36x + 48 = -28
38x + 48 = -28
38x = -28 - 48
38x = -76
x = -76/38
x = -2

Substitute the value of x back into equation (1) to solve for y:
-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6

Therefore, the solution to the system of equations is:
(x, y) = (-2, -6)
Answered by GPT 3.5
To determine how many solutions the system of equations has, we can examine the slopes of the two equations.

The given system of equations is:
6x + 2y = -18 ------(1)
3x + y = 24 ------(2)

We can rewrite equation (2) as y = -3x + 24 by subtracting 3x from both sides.

The slope of equation (1) is -3 (the coefficient of x).
The slope of equation (2) is -3 as well.

Since the two equations have the same slope, but different y-intercepts, the lines are parallel. Parallel lines never intersect, meaning there are no solutions to the system of equations.

Therefore, the system of equations has no solution.