Question

Put the steps in order that are used to solve the following systems of equations by substitution.

−7x−2y=−13

x−2y=11

Answer 1

[AI-generated answer — Bot GPT 3.5]

1. Solve one equation for one variable in terms of the other variable.

2. Substitute the expression for the variable found in step 1 into the other equation.
3. Simplify the equation obtained in step 2 by combining like terms.
4. Solve the resulting equation for the remaining variable.
5. Substitute the value found in step 4 back into one of the original equations to solve for the other variable.
6. Write the solutions as an ordered pair.

Answer 2

[AI-generated answer — Explain Bot]

To solve the system of equations by substitution, follow these steps:

Step 1: Solve one of the equations for either x or y in terms of the other variable.

In this case, let's solve the second equation (x - 2y = 11) for x:
x = 2y + 11

Step 2: Substitute the expression for x from Step 1 into the other equation.

Substitute x = 2y + 11 into the first equation (-7x - 2y = -13):
-7(2y + 11) - 2y = -13

Step 3: Simplify and solve the resulting equation for y.

-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4

Step 4: Substitute the found value of y into one of the original equations and solve for x.

Using the second equation (x - 2y = 11):
x - 2(-4) = 11
x + 8 = 11
x = 3

Step 5: Check the solution by substituting the found values of x and y into the other equation.

Substituting x = 3 and y = -4 into the first equation (-7x - 2y = -13):
-7(3) - 2(-4) = -13
-21 + 8 = -13
-13 = -13

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

Answer 3

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

To solve a system of equations by substitution, follow these steps in order:

Step 1: Solve one equation for one variable in terms of the other variable.
For example, let's solve the second equation for x:
x - 2y = 11
-> x = 2y + 11

Step 2: Substitute the expression obtained in Step 1 into the other equation.
Substitute the expression 2y + 11 for x in the first equation:
-7x - 2y = -13
-> -7(2y + 11) - 2y = -13

Step 3: Simplify and solve the resulting equation for the remaining variable.
Expand and solve the equation:
-14y - 77 - 2y = -13
-> -16y - 77 = -13
-> -16y = 64
-> y = -4

Step 4: Substitute the value of y obtained in Step 3 into either equation to solve for the other variable.
Using the second equation:
x - 2y = 11
-> x - 2(-4) = 11
-> x + 8 = 11
-> x = 3

Step 5: Check your solution by substituting the values of x and y into both original equations.
Substituting x = 3 and y = -4 into the first equation:
-7x - 2y = -13
-> - (7 * 3) - (2 * -4) = -13
-> -21 + 8 = -13
-> -13 = -13

Substituting x = 3 and y = -4 into the second equation:
x - 2y = 11
-> 3 - 2(-4) = 11
-> 3 + 8 = 11
-> 11 = 11

Both equations are satisfied, so the solution to the system of equations is x = 3 and y = -4.