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−16y−77=−13%0D%0A−%0D%0A16%0D%0A%0D%0A−%0D%0A77%0D%0A=%0D%0A−%0D%0A13%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−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−16y=64%0D%0A−%0D%0A16%0D%0A%0D%0A=%0D%0A64%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%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%0Ay=−4%0D%0A%0D%0A=%0D%0A−%0D%0A4%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(3,−4)%0D%0A(%0D%0A3%0D%0A,%0D%0A−%0D%0A4%0D%0A)

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−16y−77=−13%0D%0A−%0D%0A16%0D%0A%0D%0A−%0D%0A77%0D%0A=%0D%0A−%0D%0A13%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−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−16y=64%0D%0A−%0D%0A16%0D%0A%0D%0A=%0D%0A64%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%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%0Ay=−4%0D%0A%0D%0A=%0D%0A−%0D%0A4%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(3,−4)%0D%0A(%0D%0A3%0D%0A,%0D%0A−%0D%0A4%0D%0A)

Answer 1

1. Rewrite the first equation as x = 2y + 11.

2. Substitute the expression x = 2y + 11 into the second equation.
3. Solve the equation -7(2y + 11) - 2y = -13 for y.
4. Substitute the value of y into the expression x = 2y + 11 to solve for x.
5. The solution to the system of equations is (x, y) = (3, -4).

Answer 2

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

For example, from the first equation: x = 2y + 11

2. Substitute the expression from step 1 into the other equation.
For example, substitute x = 2y + 11 into the second equation:
(2y + 11) - 2y = 11

3. Solve the resulting equation from step 2 to find the value of the remaining variable.
In this case, solving (2y + 11) - 2y = 11 gives the value y = -4.

4. Substitute the found value of y back into the expression from step 1 to find the value of the other variable.
Using y = -4, substitute into x = 2y + 11 to find x:
x = 2(-4) + 11

5. Simplify the expression from step 4 to find the value of the remaining variable.
In this case, simplifying x = 2(-4) + 11 gives the value x = 3.

6. Write the final solution as an ordered pair (x, y).
The final solution is (3, -4).

Answer 3

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

1. Start by selecting one of the equations and solving it for one variable in terms of the other variable. Let's choose the equation "x - 2y = 11". Solving this equation for "x", you get "x = 2y + 11". This will be used later to substitute for "x" in the second equation.

2. Take the second equation, which is "-7x - 2y = -13", and substitute the value of "x" from the previous step into this equation. Substituting "x = 2y + 11", the equation becomes "-7(2y + 11) - 2y = -13".

3. Simplify the equation by distributing and combining like terms. In this case, simplify "-7(2y + 11)" to "-14y - 77" and the equation becomes "-14y - 77 - 2y = -13".

4. Continue simplifying the equation by combining like terms. In this case, simplify "-14y - 2y" to "-16y" and "-77 - 13" to "-90". The equation becomes "-16y - 90 = -13".

5. Solve the simplified equation for the remaining variable. In this case, solve "-16y - 90 = -13" for "y". Add 90 to both sides of the equation to isolate the variable: "-16y = 77". Divide both sides by -16 to solve for "y": "y = -4.8125" (approximately).

6. Substitute the value of "y" into the equation derived in step 1 ("x = 2y + 11"). Substituting "y = -4.8125", you get "x = 2(-4.8125) + 11". Simplify the expression: "x = -9.625 + 11". Combine the terms: "x = 1.375".

7. The solution to the system of equations is the ordered pair (x, y). In this case, the solution is (1.375, -4.8125).

So, the correct order of steps to solve the system of equations by substitution is as follows:
1. Select one equation and solve for one variable.
2. Substitute the value of the variable obtained in step 1 into the other equation.
3. Simplify the equation obtained in step 2.
4. Combine like terms and solve for the remaining variable.
5. Substitute the value of the solved variable into the equation obtained in step 1 and simplify.
6. Write the solution as an ordered pair (x, y).