Put the steps in order that are used to solve the following systems of equations by substitution.%0D%0A%0D%0A−7x−2y=−13%0D%0A−%0D%0A7%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A13%0D%0Ax−2y=11%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A11%0D%0A(10 points)%0D%0AArrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.%0D%0A%0D%0A−7(2y+11)−2y=−13%0D%0A−%0D%0A7%0D%0A(%0D%0A2%0D%0A%0D%0A+%0D%0A11%0D%0A)%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A13%0D%0A%0D%0A−16y=64%0D%0A−%0D%0A16%0D%0A%0D%0A=%0D%0A64%0D%0A%0D%0Ay=−4%0D%0A%0D%0A=%0D%0A−%0D%0A4%0D%0A%0D%0Ax−2y=11%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A11%0D%0A --> x=2y+11%0D%0A%0D%0A=%0D%0A2%0D%0A%0D%0A+%0D%0A11%0D%0A%0D%0A(3,−4)%0D%0A(%0D%0A3%0D%0A,%0D%0A−%0D%0A4%0D%0A)%0D%0A%0D%0Ax−2(−4)=11%0D%0A%0D%0A−%0D%0A2%0D%0A(%0D%0A−%0D%0A4%0D%0A)%0D%0A=%0D%0A11%0D%0A%0D%0A−14y−77−2y=−13%0D%0A−%0D%0A14%0D%0A%0D%0A−%0D%0A77%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A13%0D%0A%0D%0Ax+8=11%0D%0A%0D%0A+%0D%0A8%0D%0A=%0D%0A11%0D%0A%0D%0Ax=3%0D%0A%0D%0A=%0D%0A3%0D%0A%0D%0A−16y−77=−13%0D%0A−%0D%0A16%0D%0A%0D%0A−%0D%0A77%0D%0A=%0D%0A−%0D%0A13

Question

Put the steps in order that are used to solve the following systems of equations by substitution.%0D%0A%0D%0A−7x−2y=−13%0D%0A−%0D%0A7%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A13%0D%0Ax−2y=11%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A11%0D%0A(10 points)%0D%0AArrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.%0D%0A%0D%0A−7(2y+11)−2y=−13%0D%0A−%0D%0A7%0D%0A(%0D%0A2%0D%0A%0D%0A+%0D%0A11%0D%0A)%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A13%0D%0A%0D%0A−16y=64%0D%0A−%0D%0A16%0D%0A%0D%0A=%0D%0A64%0D%0A%0D%0Ay=−4%0D%0A%0D%0A=%0D%0A−%0D%0A4%0D%0A%0D%0Ax−2y=11%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A11%0D%0A --> x=2y+11%0D%0A%0D%0A=%0D%0A2%0D%0A%0D%0A+%0D%0A11%0D%0A%0D%0A(3,−4)%0D%0A(%0D%0A3%0D%0A,%0D%0A−%0D%0A4%0D%0A)%0D%0A%0D%0Ax−2(−4)=11%0D%0A%0D%0A−%0D%0A2%0D%0A(%0D%0A−%0D%0A4%0D%0A)%0D%0A=%0D%0A11%0D%0A%0D%0A−14y−77−2y=−13%0D%0A−%0D%0A14%0D%0A%0D%0A−%0D%0A77%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A13%0D%0A%0D%0Ax+8=11%0D%0A%0D%0A+%0D%0A8%0D%0A=%0D%0A11%0D%0A%0D%0Ax=3%0D%0A%0D%0A=%0D%0A3%0D%0A%0D%0A−16y−77=−13%0D%0A−%0D%0A16%0D%0A%0D%0A−%0D%0A77%0D%0A=%0D%0A−%0D%0A13

Answer 1

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

2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into the expression found in step 1 to solve for the first variable.
5. Write the solution as an ordered pair (x, y).

Answer 2

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

1. Start by choosing one of the equations and solving for one variable in terms of the other. Let's choose the second equation, which is x - 2y = 11. Solve for x: x = 2y + 11.

2. Take the solved equation from step 1 and substitute it into the other equation. Replace x in the first equation with 2y + 11: -7x - 2y = -13 becomes -7(2y + 11) - 2y = -13.

3. Simplify and solve the resulting equation from step 2. Use the distributive property to expand -7(2y + 11) = -14y - 77. The equation now becomes -14y - 77 - 2y = -13.

4. Combine like terms and solve for y. Bring the y terms together: -14y - 77 - 2y = -13 becomes -16y - 77 = -13. Then, isolate the variable by adding 77 to both sides: -16y - 77 + 77 = -13 + 77. Simplify: -16y = 64.

5. Solve for y by dividing both sides of the equation by -16: y = 64 / -16. Simplify: y = -4.

6. Substitute the value of y back into the solved equation from step 1 to find the value of x. Use x = 2y + 11, where y is -4: x = 2(-4) + 11. Simplify: x = -8 + 11.

7. Calculate the value of x: x = 3.

Therefore, the solution to the system of equations is x = 3 and y = -4, or (3,-4) as an ordered pair.

Answer 3

Here are the steps in the correct order to solve the given system of equations by substitution:

1. Rewrite the first equation in terms of one variable (x or y). In this case, rewrite the first equation as: x = 2y + 11.
2. Substitute the expression for x from step 1 into the second equation. Replace x in the second equation with 2y + 11. The equation becomes: (2y + 11) - 2y = 11.
3. Solve the equation from step 2 for y. Simplify the equation: 2y + 11 - 2y = 11. The y terms cancel out, leaving 11 = 11.
4. Determine the value of y. Since the equation from step 3 simplifies to 11 = 11, this means that y can take any value and will not affect the outcome of the system of equations.
5. Substitute the value of y into the expression for x from step 1. Using the expression x = 2y + 11, substitute y = -4 to find x. The equation becomes: x = 2(-4) + 11.
6. Solve the equation from step 5 for x. Simplify the equation: x = -8 + 11.
7. Determine the value of x. In step 6, x simplifies to x = 3.
8. Write the solution as an ordered pair (x, y). The solution to the system of equations is (3, -4).

The correct order of steps is:

1. x = 2y + 11
2. (2y + 11) - 2y = 11
3. 11 = 11
4. y can take any value
5. x = 2y + 11
6. x = -8 + 11
7. x = 3
8. (3, -4)