Put these steps into order that are used to solve the following systems of equations by substitution.
-7x -2y = - 13
x - 2y = 11
(Put the numbers below in order. ONLY use the numbers listed.)
• -7(2y+11)-2y=-13
• x+8=11
• x - 2y = 11 —> x = 2y + 11
• -16y - 77 = -13
• x = 3
• -14y - 17 -2y = -13
• y = -4
• -16y = 64
• x - 2 (-4) = 11
• (3,-4)
1. x - 2y = 11 —> x = 2y + 11
2. -7x - 2y = -13
3. Substitute x = 2y + 11 into equation 2: -7(2y + 11) - 2y = -13
4. Simplify Step 3: -14y - 77 - 2y = -13
5. Combine like terms in Step 4: -16y - 77 = -13
6. Add 77 to both sides in Step 5: -16y = 64
7. Divide both sides by -16 in Step 6: y = -4
8. Substitute y = -4 into equation 1: x - 2(-4) = 11
9. Simplify Step 8: x + 8 = 11
10. Subtract 8 from both sides in Step 9: x = 3
11. The solution to the system of equations is (x, y) = (3, -4)
The correct order of steps to solve the system of equations by substitution is as follows:
1. x - 2y = 11 —> x = 2y + 11
2. Substitute the value of x from step 1 into the other equation:
-7x - 2y = -13
-7(2y + 11) - 2y = -13
3. Simplify the equation from step 2:
-16y - 77 = -13
4. Solve for y:
-16y = 64
y = -4
5. Substitute the value of y from step 4 into the equation x = 2y + 11:
x = 2(-4) + 11
x = 3
6. Find the solution by combining the values of x and y:
(3, -4)
To solve the given system of equations by substitution, follow these steps:
1. Begin with the two given equations:
-7x - 2y = -13
x - 2y = 11
2. Solve one of the equations for one of the variables. In this case, let's solve the second equation for x:
x = 2y + 11
3. Substitute the expression for x (from step 2) into the other equation. Replace x with 2y + 11 in the first equation:
-7(2y + 11) - 2y = -13
4. Simplify and solve for y:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
5. Substitute the value of y (from step 4) into one of the original equations to solve for x. Using the second equation:
x - 2(-4) = 11
x + 8 = 11
x = 3
6. The solution to the system of equations is the ordered pair (x, y). Thus, the solution is (3, -4).
Putting the steps in order:
1. Begin with the given equations.
2. Solve one equation for one variable.
3. Substitute the expression for that variable into the other equation.
4. Simplify and solve for the remaining variable.
5. Substitute the value of the remaining variable back into one of the original equations.
6. The solution is the ordered pair (x, y).