Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11
1. Start by solving one of the equations for one variable in terms of the other variable. In this case, you could solve the second equation for x in terms of y:
x = 2y + 11
2. Substitute the expression for x from step 1 into the other equation.
-7(2y + 11) - 2y = -13
3. Simplify and solve for y.
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
4. Substitute the value of y from step 3 into one of the original equations to solve for x. Let's use the second equation:
x - 2(-4) = 11
x + 8 = 11
x = 3
5. The solution to the system of equations is x = 3, y = -4.
The steps to solve a system of equations by substitution are as follows:
1. Solve one of the equations for one variable in terms of the other variable.
In this case, let's solve the second equation, x - 2y = 11, for x:
x = 2y + 11
2. Substitute the expression found in step 1 into the other equation.
Substitute x = 2y + 11 into the first equation, -7x - 2y = -13:
-7(2y + 11) - 2y = -13
3. Simplify and solve the resulting equation for the remaining variable.
Distribute -7 to 2y + 11:
-14y - 77 - 2y = -13
Combine like terms:
-16y - 77 = -13
Add 77 to both sides:
-16y = 64
Divide both sides by -16:
y = -4
4. Substitute the value of y found in step 3 into one of the original equations to solve for the other variable.
Substitute y = -4 into x - 2y = 11:
x - 2(-4) = 11
Simplify:
x + 8 = 11
Subtract 8 from both sides:
x = 3
Therefore, the solution to the system of equations −7x − 2y = −13 and x - 2y = 11 is x = 3 and y = -4.
To solve a system of equations by substitution, here are the steps:
Step 1: Choose one equation from the system and solve it for one variable in terms of the other variable. Let's choose the second equation: x - 2y = 11. Solve this equation for x:
x = 2y + 11. (Equation A)
Step 2: Substitute the expression you found for x in Equation A into the other equation in the system.
Substituting x = 2y + 11 into the first equation: -7(2y + 11) - 2y = -13.
Step 3: Simplify and solve the resulting equation for y.
-14y - 77 - 2y = -13.
Combine like terms: -16y - 77 = -13.
Step 4: Continue to solve for y.
Add 77 to both sides of the equation: -16y = 64.
Divide both sides by -16: y = -4.
Step 5: Substitute the value of y in the equation you solved for in Step 1 to find the corresponding value of x.
Using Equation A: x = 2(-4) + 11.
x = -8 + 11.
x = 3.
Step 6: Write the solution as an ordered pair (x, y).
The solution to the system of equations is (3, -4).