Put the steps in order that are used to solve the following systems of equations by substitution.
-7x-2y= -13
x-2y = 11
-16y = 64
= x-2y = 11 --> x = 2y + 11
-14y - 77 - 2y = - 13
-7(2y + 11) - 2y = - 13
(3, -4)
-16у - 77 = -13
x + 8 = 11
y = -4
x = 3
x - 2 (-4) = 11
Put the steps above in the right order, only use the numbers I listed above.
1. -7x-2y= -13
2. x-2y = 11
3. Solve equation 2 for x: x = 2y + 11
4. Substitute x in equation 1 with 2y + 11: -7(2y + 11) - 2y = - 13
5. Simplify the equation: -14y - 77 - 2y = - 13
6. Combine like terms: -16y - 77 = -13
7. Solve for y: -16y = 64
8. Divide both sides by -16: y = -4
9. Substitute y = -4 in equation 2: x - 2(-4) = 11
10. Simplify the equation: x + 8 = 11
11. Solve for x: x = 3
12. The solution to the system of equations is (x, y) = (3, -4)
1. -7x - 2y = -13
2. x - 2y = 11
3. x = 2y + 11
4. Substitute the expression for x from step 3 into equation 1 to solve for y: -7(2y + 11) - 2y = -13
5. Simplify the equation from step 4: -14y - 77 - 2y = -13
6. Combine like terms in the equation from step 5: -16y - 77 = -13
7. Add 77 to both sides of the equation from step 6 and simplify: -16y = 64
8. Solve for y by dividing both sides of the equation from step 7 by -16: y = -4
9. Substitute the value of y from step 8 into the expression for x from step 3: x = 2(-4) + 11
10. Simplify the expression from step 9: x = 3
11. Verify the solution by substituting the values of x and y from steps 9 and 8, respectively, into equation 2: 3 - 2(-4) = 11
To put the steps in the correct order, we need to arrange them based on the logic of solving the system of equations by substitution. Here is the correct order:
1. Start with the given system of equations:
-7x - 2y = -13
x - 2y = 11
2. Solve one of the equations for one variable in terms of the other variable. Here, we can solve the second equation for x:
x = 2y + 11
3. Substitute the expression found in step 2 for the variable in the other equation. In this case, substitute x with 2y + 11 in the first equation:
-7(2y + 11) - 2y = -13
4. Simplify and solve the resulting equation for the remaining variable. Distribute -7 to 2y and 11:
-14y - 77 - 2y = -13
5. Combine like terms on the left side of the equation:
-16y - 77 = -13
6. Isolate the variable by moving constant terms to the other side of the equation:
-16y = -13 + 77
7. Simplify further:
-16y = 64
8. Divide both sides of the equation by -16 to solve for y:
y = -4
9. Substitute the value found in step 8 back into one of the original equations to find the corresponding value of x. Using the second equation:
x - 2(-4) = 11
10. Simplify and solve for x:
x + 8 = 11
11. Isolate x by moving 8 to the other side of the equation:
x = 11 - 8
12. Simplify further:
x = 3
Therefore, the solution to the given system of equations is (x, y) = (3, -4).