Put the steps in order that are used to solve the following systems of equations by substitution.
-72-24= -13
x-2y = 11
Since the equations provided do not form a system, I will assume they are separate equations to solve individually.
First, let's solve the equation -72 - 24 = -13:
-72 - 24 = -13
-96 = -13
Since -96 is not equal to -13, this equation has no solution.
Next, let's solve the equation x - 2y = 11:
1. Solve one equation for one variable in terms of the other variable. In this case, we can solve x - 2y = 11 for x:
x = 2y + 11
2. Substitute the expression found for x in step 1 into the other equation. Since there is no other equation provided, we cannot proceed with substitution in this case.
Therefore, the steps to solve the system of equations by substitution cannot be applied here, as the equations provided do not form a system.
To solve the system of equations by substitution, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable.
For example, rearrange the second equation x - 2y = 11 to solve for x: x = 11 + 2y.
2. Substitute the expression for the solved variable (x in this case) into the other equation.
Replace x in the first equation -72 - 24 = -13 with the expression (11 + 2y): -72 - 24 = -13.
3. Simplify the equation and solve for the remaining variable (y).
Continuing from step 2: -96 = -13.
4. Solve the simplified equation for y by isolating the variable.
Subtracting -13 from both sides: -96 + 13 = y.
5. Calculate the value of y.
Simplifying: -83 = y.
6. Substitute the calculated value of y back into one of the original equations.
Using the first equation -72 - 24 = -13, replace y with -83: -72 - 24(-83) = -13.
7. Solve the equation for x.
Simplifying: -72 + 1992 = -13.
8. Calculate the value of x.
Simplifying: 1920 = x.
Therefore, the solution to the system of equations is x = 1920 and y = -83.
To solve a system of equations by substitution, you can follow these steps:
Step 1: Choose one of the equations to solve for one variable in terms of the other variable. In this case, let's solve the second equation, x - 2y = 11, for x.
x = 2y + 11
Step 2: Substitute the expression for x obtained in Step 1 into the other equation in the system. We substitute x = 2y + 11 into the first equation, which is -72 - 24 = -13.
-72 - 24 = 2y + 11 - 13
Simplifying this equation gives us:
-96 = 2y - 2
Step 3: Solve the resulting equation from Step 2 for the remaining variable, in this case, y.
To solve for y, we'll isolate the term with y:
-96 + 2 = 2y
-94 = 2y
Dividing both sides of the equation by 2:
y = -47
Step 4: Substitute the value of y found in Step 3 back into one of the original equations to solve for the other variable. Let's substitute y = -47 into the second equation, x - 2y = 11.
x - 2(-47) = 11
x + 94 = 11
Step 5: Solve this equation for x.
Subtracting 94 from both sides gives us:
x = 11 - 94
x = -83
Step 6: Write the solution as an ordered pair (x, y).
The solution to the system of equations is (-83, -47).