Put the steps in order that are used to solve the following system of equations by substitution.
-7x-2y=-13 x-2y=11
1. Solve one of the equations for one variable (in this case, solve the second equation for x): x = 2y + 11.
2. Substitute the expression of one variable into the other equation (substitute x in the first equation with 2y + 11): -7(2y + 11) - 2y = -13.
3. Simplify and solve the resulting equation for the remaining variable (in this case, solve for y): -14y - 77 - 2y = -13.
4. Solve for y: -16y - 77 = -13.
5. Solve for y: -16y = 64.
6. Solve for y: y = -4.
7. Substitute the value of y back into one of the original equations (use the second equation): x - 2(-4) = 11.
8. Simplify and solve for x: x + 8 = 11.
9. Solve for x: x = 3.
10. The solution to the system of equations is x = 3 and y = -4.
To solve the system of equations by substitution, follow these steps in order:
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve equation 2 for x:
x - 2y = 11
x = 2y + 11
Step 2: Substitute the expression obtained in Step 1 into the other equation. Substitute x = 2y + 11 into equation 1:
-7(2y + 11) - 2y = -13
Step 3: Simplify and solve the resulting equation for the remaining variable. Distribute -7 to 2y and 11 in equation 3:
-14y - 77 - 2y = -13
-16y - 77 = -13
Step 4: Solve this equation for y:
-16y = -13 + 77
-16y = 64
y = 64 / -16
y = -4
Step 5: Substitute the value found in Step 4 back into equation 2 to solve for x:
x - 2(-4) = 11
x + 8 =11
x = 11 - 8
x = 3
Therefore, the solution to the system of equations is x = 3 and y = -4.
To solve the system of equations by substitution, follow these steps:
1. Begin by solving one of the equations for one variable in terms of the other variable. Let's solve the second equation (x - 2y = 11) for x:
x = 2y + 11
2. Substitute the expression for x from step 1 into the other equation (-7x - 2y = -13):
-7(2y + 11) - 2y = -13
3. Simplify the equation by distributing -7 to 2y and 11:
-14y - 77 - 2y = -13
4. Combine like terms on the left side of the equation:
-16y - 77 = -13
5. Add 77 to both sides of the equation to isolate the variable term:
-16y = 64
6. Divide both sides of the equation by -16 to solve for y:
y = -4
7. Substitute the value of y into either of the original equations to solve for x. Let's substitute it into the second equation:
x - 2(-4) = 11
8. Simplify the equation:
x + 8 = 11
9. Subtract 8 from both sides of the equation to isolate the variable term:
x = 3
So, the solution to the system of equations is x = 3 and y = -4.