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%0Ax=3%0D%0A%0D%0A=%0D%0A3%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%0A(3,−4)%0D%0A(%0D%0A3%0D%0A,%0D%0A−%0D%0A4%0D%0A)%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%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%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%0Ax+8=11%0D%0A%0D%0A+%0D%0A8%0D%0A=%0D%0A11%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
1) Set one equation equal to one variable, typically solving for x or y.
2) Substitute the expression from step 1 into the other equation.
3) Solve the resulting equation from step 2 for the remaining variable.
4) Substitute the value of the remaining variable into the expression from step 1 to find the value of the other variable.
5) Write the solution as an ordered pair (x, y).
The steps to solve the given system of equations by substitution are as follows:
1. Choose one of the equations and solve it for one variable in terms of the other variable. Let's choose the equation x - 2y = 11. Solving for x, we get x = 2y + 11.
2. Substitute the expression for the variable that was solved in step 1 into the other equation. Let's substitute x = 2y + 11 into the equation -7x - 2y = -13.
3. Simplify and solve the resulting equation. Substituting x = 2y + 11 into -7x - 2y = -13, we get -7(2y + 11) - 2y = -13. Expanding and simplifying this equation, we get -14y - 77 -2y = -13.
4. Solve the equation obtained in step 3 for the remaining variable. In this case, we have -16y - 77 = -13. Solving for y, we get -16y = 64, which means y = -4.
5. Substitute the value of y obtained in step 4 into one of the original equations to find the value of the other variable. Let's substitute y = -4 into x - 2y = 11. We get x - 2(-4) = 11, which simplifies to x + 8 = 11. Solving for x, we find x = 3.
So the solution to the system of equations is x = 3 and y = -4.
To solve the system of equations by substitution, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
- In this case, let's solve the second equation for x:
x - 2y = 11
x = 2y + 11
Step 2: Substitute the expression for the solved variable in the other equation.
- Replace x in the first equation with 2y + 11:
-7(2y + 11) - 2y = -13
Step 3: Simplify and solve the resulting equation for the remaining variable.
- Distribute and combine like terms:
-14y - 77 - 2y = -13
-16y - 77 = -13
Step 4: Solve for y:
- Add 77 to both sides:
-16y = 64
- Divide by -16:
y = -4
Step 5: Substitute the value of y back into one of the original equations and solve for the other variable.
- Let's use the first equation:
-7x - 2(-4) = -13
-7x + 8 = -13
Step 6: Solve for x:
- Subtract 8 from both sides:
-7x = -21
- Divide by -7:
x = 3
Therefore, the solution to the system of equations is x = 3 and y = -4.