Question
Put the steps in order that are used to solve the following systems of equations by substitution.
−7x−2y=−13
x−2y=11
(10 points)
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1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the expression from 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 one of the original equations to solve for the other variable.
5. Write the solution as an ordered pair (x, y).
1. Solve one of the equations 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 either of the original equations to find the value of the other variable.
5. Write the solution as an ordered pair (x, y), where x and y are the values found in step 3 and step 4, respectively.
To solve a system of equations by substitution, you can follow these steps:
1. Choose one of the equations and solve it for one variable in terms of the other variable. In this case, let's choose the second equation and solve it for x:
x - 2y = 11
Subtracting 2y from both sides, we get:
x = 2y + 11
2. Substitute this expression for x in the other equation. In this case, substitute 2y + 11 for x in the first equation:
-7x - 2y = -13
-7(2y + 11) - 2y = -13
3. Simplify and solve the resulting equation for y:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
Dividing both sides by -16, we get:
y = -4
4. Substitute this value of y back into one of the original equations to solve for x. Let's use the second equation:
x - 2(-4) = 11
x + 8 = 11
Subtracting 8 from both sides, we get:
x = 3
Therefore, the solution to the system of equations is x = 3 and y = -4.
its not the answer
Apologies for the incorrect response. Here is the correct order of steps to solve the system of equations by substitution:
1. Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:
x = 2y + 11
2. Substitute the expression found in step 1 into the other equation. Substitute 2y + 11 for x in the first equation:
-7(2y + 11) - 2y = -13
3. Simplify and solve the resulting equation for the remaining variable. Solve for y:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
4. Substitute the value found in step 3 back into either of the original equations to find the value of the other variable. Let's substitute y = -4 into the second equation:
x - 2(-4) = 11
x + 8 = 11
x = 3
5. Write the solution as an ordered pair (x, y), where x is the value found in step 4 and y is the value found in step 3. The solution to the system of equations is (3, -4).