Put the steps in order that are used to solve the following systems of equations by substitution.
x - 2y = 11 --> x = 2y + 11
-16y = 64
-16y - 77 = -13
x - 2(-4) = 11
x + 8 = 11
y = -4
x = 3
-14y - 77 -2y = -13
-7 (2y + 11) -2y = -13
(3, -4)
1. x = 2y + 11 (rearrange the first equation)
2. Substitute x = 2y + 11 into the second equation: -16y = 64
3. Solve for y: y = -4
4. Substitute y = -4 into x = 2y + 11: x = 3
5. Check solution by substituting x = 3 and y = -4 into both original equations
6. Final solution: (x, y) = (3, -4)
Here are the steps in the correct order to solve the system of equations by substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable. In this case, we can solve the first equation, x - 2y = 11, for x to get x = 2y + 11.
Step 2: Substitute the expression for one variable from step 1 into the other equation(s) in the system. We will substitute x = 2y + 11 into the second and third equations.
Step 3: Solve the resulting equation(s) for the remaining variable.
For the second equation, -16y = 64, we can divide both sides by -16 to solve for y, giving us y = -4.
For the third equation, -16y - 77 = -13, we can simplify by combining like terms (-16y and -77) and then adding 77 to both sides to isolate the term with y. This gives us -16y = 64, and we can divide both sides by -16 to solve for y, which again gives us y = -4.
Step 4: Substitute the value found in step 3 back into one of the original equations to solve for the other variable. We can substitute y = -4 into the equation x = 2y + 11. This gives us x = 2(-4) + 11, which simplifies to x = 3.
Step 5: Check the solution by substituting the values of x and y into the remaining equations to see if they satisfy both equations. Let's substitute x = 3 and y = -4 into the first equation, x - 2y = 11. We get 3 - 2(-4) = 11, which simplifies to 3 + 8 = 11, and that is true.
Therefore, 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:
x - 2y = 11 ---> (Equation 1)
-16y = 64 ---> (Equation 2)
2. Solve Equation 2 for y:
-16y = 64
Divide both sides by -16:
y = -64 / -16
Simplify:
y = 4
3. Substitute the found value of y (y = 4) into Equation 1:
x - 2y = 11
x - 2(4) = 11
x - 8 = 11
Add 8 to both sides:
x = 11 + 8
x = 19
4. The solution to the system of equations is the pair (x, y), so the solution is (19, 4).
So, the correct order of steps to solve the given system of equations by substitution is:
-16y = 64
y = 4
x - 2(4) = 11
x = 19
(19, 4)