Question

Solve the system of equations.

8x−3y= −22
y=10+4x

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can substitute the value of y from the second equation into the first equation and solve for x.

y = 10 + 4x

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 solve for 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 2

[AI-generated answer — Step-by-Step Bot]

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

Step 1: Start with the second equation, y = 10 + 4x.

Step 2: Substitute this value of y into the first equation.

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

Step 3: Distribute the -3.

8x - 30 - 12x = -22

Step 4: Combine like terms.

-4x - 30 = -22

Step 5: Add 30 to both sides of the equation.

-4x - 30 + 30 = -22 + 30

-4x = 8

Step 6: Divide both sides of the equation by -4.

(-4x) / -4 = 8 / -4

x = -2

Step 7: Now that we have the value of x, substitute this into either of the original equations to solve for y. Let's use the second equation, y = 10 + 4x.

y = 10 + 4(-2)

y = 10 - 8

y = 2

Step 8: Therefore, the solution to the system of equations is x = -2 and y = 2.

Answer 3

[AI-generated answer — Explain Bot]

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

First, we'll solve one of the equations for one variable in terms of the other variable. We'll solve the second equation for y in terms of x.
y = 10 + 4x

Next, we'll substitute this expression for y in the first equation.
8x - 3(10 + 4x) = -22

Now, we'll distribute the -3 to simplify the equation.
8x - 30 - 12x = -22

Combine like terms.
(8x - 12x) - 30 = -22
-4x - 30 = -22

Add 30 to both sides of the equation to isolate the variable.
-4x - 30 + 30 = -22 + 30
-4x = 8

Next, divide both sides of the equation by -4 to solve for x.
-4x / -4 = 8 / -4
x = -2

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the second equation.
y = 10 + 4x
y = 10 + 4(-2)
y = 10 - 8
y = 2

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