Solve the system of equations

8X-3y=-22
y=10+4x

Answers

Answer
Write it as this (__,__)
Solve the systems of equations
5x+2y=14
x-6y=22
Solve the system of equations
-9x+y=12
2x+4y=-28
Answer
No decimals
Answer
How many solutions does the system of equations have?
6x+2y=-18
3X+y=24
Answered by GPT 3.5
To solve this system of equations, we can substitute the value of y from the second equation into the first equation.

Substitute y = 10 + 4x into the first equation:
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = 8
x = -2

Now substitute the value of x back into the second equation to find the value of y:
y = 10 + 4(-2)
y = 10 - 8
y = 2

Therefore, the solution to the system of equations is x = -2 and y = 2.
Answered by GPT 3.5
The solution to the system of equations is (-2, 2).
Answered by GPT 3.5
To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of substitution.

First, solve the second equation for x:
x = 22 + 6y

Now, substitute the expression for x into the first equation:
5(22 + 6y) + 2y = 14
110 + 30y + 2y = 14
32y = -96
y = -3

Now, substitute y = -3 back into the second equation to solve for x:
x - 6(-3) = 22
x + 18 = 22
x = 4

Therefore, the solution to the system of equations is x = 4 and y = -3, written as (4, -3).
Answered by GPT 3.5
To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we will multiply the first equation by 4 and the second equation by 1 to create opposite coefficients for y:

-36x + 4y = 48
2x + 4y = -28

Adding the two equations together, we get:

-34x = 20
x = -20/34
x = -10/17

Now, substitute x = -10/17 into the first equation to solve for y:

-9(-10/17) + y = 12
90/17 + y = 12
y = 12 - 90/17
y = (204 - 90) / 17
y = 114 / 17
y = 6.7 (rounded to one decimal place)

Therefore, the solution to the system of equations is x = -10/17 and y = 6.7, written as (-10/17, 6.7) or approximately (-0.59, 6.7).
Answered by GPT 3.5
To solve the system of equations -9x+y=12 and 2x+4y=-28, we can use the elimination method.

First, let's multiply the first equation by 4 to have a 4y term in both equations:

-36x + 4y = 48
2x + 4y = -28

Now, we will subtract the second equation from the first equation to eliminate the y term:

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

Now that we have found the value of x, we can substitute it back into the first equation 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 = -2 and y = -6, written as (-2, -6).
Answered by GPT 3.5
To determine the number of solutions the system of equations has, we can analyze the coefficients of x and y in the equations.

The first equation is 6x + 2y = -18. By dividing the whole equation by 2, we get 3x + y = -9. This equation can be rewritten as 3x + y = -9.

The second equation is 3x + y = 24.

When we compare these two equations, we can see that they represent two parallel lines, as the coefficients of x and y are the same in both equations, but the constants on the right side of the equal sign are different (one is -9, and the other is 24).

Since the equations represent lines that are parallel, they will never intersect, and there is no solution. This system of equations is inconsistent and has 0 solutions.

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