Put the steps in order that are used to solve the following systems of equations by substitution.
-7x-2y=-13
x-2y=11
| x-2y=11-->x=2y+11, -16y=64, x+8=11, -14y-77-2y=-13, -7(2y+11)-2y=-13, x-2(-4)=11, x=3, y=-4, -16y-77=-13, (3,-4)
Use all the following systems
1. Write one of the equations in terms of one variable (in this case, x or y).
2. Substitute the expression for that variable into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of the remaining variable into the expression you found in step 1.
5. Solve for the variable in step 1.
6. Plug the value of the variable from step 5 into one of the original equations to find the value of the other variable.
7. Write the solution as an ordered pair (x, y).
To solve the given systems of equations using substitution, follow these steps:
Step 1: Rearrange one of the equations to express one variable in terms of the other.
For example, in the given systems:
-7x - 2y = -13 ...........(Equation 1)
x - 2y = 11 ...........(Equation 2)
We can rearrange Equation 2 to express x in terms of y:
x = 2y + 11
Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x (2y + 11) into Equation 1:
-7(2y + 11) - 2y = -13
Step 3: Solve the resulting equation for the remaining variable.
Simplify and solve for y:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
Step 4: Substitute the value of y back into the expression from Step 1 to find the value of x.
Using the equation x = 2y + 11:
x = 2(-4) + 11
x = -8 + 11
x = 3
Step 5: Verify the solution by substituting the values of x and y into both original equations.
Substituting x = 3 and y = -4 into Equation 1:
-7(3) - 2(-4) = -13
-21 + 8 = -13
-13 = -13 (True)
Substituting x = 3 and y = -4 into Equation 2:
3 - 2(-4) = 11
3 + 8 = 11
11 = 11 (True)
The solution to the given system of equations is x = 3 and y = -4, or in ordered pair form, (3, -4).
To solve a system of equations by substitution, you can follow these steps:
1. Choose one equation and solve it for a variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into the expression obtained in step 1 to find the value of the first variable.
5. Check your solution by substituting the values of the variables back into both original equations.
Now, let's apply these steps to the given system of equations:
-7x - 2y = -13 -----(Equation 1)
x - 2y = 11 -----(Equation 2)
Step 1: From Equation 2, solve for x in terms of y:
x = 2y + 11
Step 2: Substitute the expression (2y + 11) for x in Equation 1:
-7(2y + 11) - 2y = -13
Step 3: Simplify and solve the resulting equation for y:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
Step 4: Substitute the value of y (-4) into the expression x = 2y + 11 to find x:
x = 2(-4) + 11
x = -8 + 11
x = 3
Step 5: Check the solution by substituting the values of x and y into both original equations:
For Equation 1:
-7(3) - 2(-4) = -13
-21 + 8 = -13
-13 = -13
For Equation 2:
3 - 2(-4) = 11
3 + 8 = 11
11 = 11
The solution to the system of equations is x = 3 and y = -4, or (3, -4).