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 numbers
1. Start with the given system of equations:
-7x - 2y = -13
x - 2y = 11
2. Choose one of the equations to solve for one variable in terms of the other. In this case, choose the second equation and solve for x:
x = 2y + 11
3. Substitute this expression for x 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. Add 77 to both sides of the equation:
-16y = 64
7. Divide both sides by -16:
y = -4
8. Now that we have found the value of y, substitute it back into the expression for x:
x = 2(-4) + 11
x = 3
9. The solution to the system of equations is the ordered pair (x, y) = (3, -4).
To solve the system of equations by substitution, follow these steps in order:
1. Choose one of the equations and solve it for one variable in terms of the other variable. Let's choose the second equation:
x - 2y = 11
x = 2y + 11
2. Substitute the expression you found for one variable in the other equation. Let's substitute x = 2y + 11 into the first equation:
-7x - 2y = -13
-7(2y + 11) - 2y = -13
3. Solve the resulting equation for the remaining variable. Simplify the equation:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
4. Substitute the value of y back into one of the original equations to find the value of x. Let's use the equation x = 2y + 11:
x = 2(-4) + 11
x = 3
5. Verify the values of x and y by substituting them into the other equation:
x - 2y = 11
3 - 2(-4) = 11
3 + 8 = 11
11 = 11
Therefore, the solution to the system of equations is x = 3 and y = -4, or (3, -4).
To solve the given system of equations -7x - 2y = -13 and x - 2y = 11 using the substitution method, follow these steps:
Step 1: Choose one of the equations to solve for one variable in terms of the other.
We will choose the second equation: x - 2y = 11
Solve this equation for x:
x = 2y + 11
Step 2: Substitute the expression we found for x (2y + 11) into the other equation.
-7x - 2y = -13
-7(2y + 11) - 2y = -13
Simplify the equation:
-14y - 77 - 2y = -13
-16y - 77 = -13
Step 3: Solve the resulting equation for the variable.
-16y - 77 = -13
Add 77 to both sides:
-16y - 77 + 77 = -13 + 77
-16y = 64
Divide both sides by -16 to isolate y:
y = 64 / -16
Simplify the expression:
y = -4
Step 4: Substitute the value of y (-4) back into the expression we found for x (2y + 11) to find x:
x = 2(-4) + 11
x = -8 + 11
x = 3
Step 5: Write the solution as an ordered pair (x, y).
The solution is (3, -4).
Therefore, the steps to solve the given system of equations by substitution are:
1. Solve one of the equations for one variable in terms of the other.
2. Substitute the expression obtained in Step 1 into the other equation.
3. Solve the resulting equation for the variable.
4. Substitute the value of the variable back into the expression obtained in Step 1 to find the value of the other variable.
5. Write the solution as an ordered pair.