Put the steps in order that are used to solve the following systems of equations by substitution.
-7х - 2y = -13
x-2y = 11
(Put the numbers listed below in order that are used to solve this equation)
x+8 = 11
X = 3
-14y - 77 - 2y = -13
(3, -4)
-16y - 77 = -13
-16y = 64
x-2y=11–>x=2y+11
-7(2y + 11) - 2y = -13
y = -4
x - 2 (-4) = 11
1. x-2y=11–>x=2y+11
2. Substitute the value of x into the first equation: -7(2y + 11) - 2y = -13
3. Simplify the equation: -14y - 77 - 2y = -13
4. Combine like terms: -16y - 77 = -13
5. Move the constant term to the other side: -16y = 64
6. Solve for y: y = -4
7. Substitute the value of y into the second equation: x - 2 (-4) = 11
8. Simplify the equation: x + 8 = 11
9. Solve for x: x = 3
10. The solution to the system of equations is (3, -4)
The correct order of steps to solve the systems of equations by substitution is as follows:
1. x - 2y = 11
2. Rewrite one of the equations to solve for x (in terms of y): x = 2y + 11
3. Substitute the expression for x from step 2 into the other equation: -7(2y + 11) - 2y = -13
4. Simplify the equation: -14y - 77 - 2y = -13
5. Combine like terms: -16y - 77 = -13
6. Move the constant term to the other side: -16y = 64
7. Solve for y: y = -4
8. Substitute the value of y into the equation from step 2 to find x: x - 2(-4) = 11
9. Simplify the equation: x + 8 = 11
10. Move the constant term to the other side: x = 3
11. The solution to the system of equations is (x, y) = (3, -4)
To solve the system of equations by substitution, follow these steps in 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:
Solve the second equation for x:
x = 2y + 11
3. Substitute the expression for the variable found in step 2 into the other equation:
Substitute 2y + 11 for x in the first equation:
-7(2y + 11) - 2y = -13
4. Simplify and solve the resulting equation for the remaining variable:
Expand and simplify the equation:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
5. Substitute the obtained solution for the variable back into one of the original equations to find the value of the other variable:
Substitute y = -4 into the second equation:
x - 2(-4) = 11
x + 8 = 11
x = 3
6. Write the solution as an ordered pair (x, y):
The solution to the system of equations is (x, y) = (3, -4).
Therefore, the correct order of steps to solve the given system of equations by substitution is:
2, 3, 4, 5, 6.