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).
1. Solve one of the equations for one variable in terms of the other variable. In this case, we solve the second equation for x: x = 2y + 11.
2. Substitute the expression found in step 1 into the other equation. Substitute x = 2y + 11 into the first equation: -7(2y + 11) - 2y = -13.
3. Simplify the resulting equation and solve for y. -14y - 77 - 2y = -13. Combine like terms: -16y - 77 = -13.
4. Solve the equation obtained in step 3 for y. -16y - 77 = -13. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
5. Substitute the value of y obtained in step 4 into any of the original equations to solve for x. Using the second equation: x - 2(-4) = 11. Simplify: x + 8 = 11.
6. Solve the equation obtained in step 5 for x. Subtract 8 from both sides: x = 3.
7. Write the solution as an ordered pair (x, y). The solution is (3, -4).
To solve the system of equations by substitution, here are the steps in the correct order:
1. Start with the equations:
-7x - 2y = -13
x - 2y = 11
2. Solve one of the equations for either variable. Let's solve the second equation for x:
x = 2y + 11
3. Substitute the expression for x into the first equation:
-7(2y + 11) - 2y = -13
4. Simplify the equation:
-14y - 77 - 2y = -13
5. Combine like terms:
-16y - 77 = -13
6. Move constant term to the other side:
-16y = -13 + 77
7. Simplify:
-16y = 64
8. Solve for y:
y = 64 / -16
= -4
9. Substitute the value of y back into the equation x = 2y + 11:
x = 2(-4) + 11
= -8 + 11
= 3
10. The solution to the system of equations is x = 3, y = -4.
To solve the system of equations by substitution, you need to follow these steps in order:
1. Choose one of the equations and solve it for one variable in terms of the other.
In this case, let's choose the second equation x - 2y = 11 and solve it for x:
x = 2y + 11.
2. Substitute the expression for the variable you solved in step 1 into the other equation.
Replace x in the first equation -7x - 2y = -13 with the expression 2y + 11:
-7(2y + 11) - 2y = -13.
3. Simplify the equation you obtained in step 2 and solve it for the remaining variable.
Distribute -7 to 2y and 11:
-14y - 77 - 2y = -13.
Combine like terms:
-16y - 77 = -13.
Add 77 to both sides of the equation:
-16y = 64.
Divide both sides by -16 to isolate y:
y = -4.
4. Substitute the value of the variable you found in step 3 back into the expression for the other variable.
Substitute y = -4 into the expression x = 2y + 11:
x = 2(-4) + 11.
Simplify:
x = 3.
5. Check the solution by substituting the values of x and y back into the original equations.
Substitute x = 3 and y = -4 into the first equation -7x - 2y = -13:
-7(3) - 2(-4) = -13.
Simplify:
-21 + 8 = -13.
-13 = -13.
Therefore, the solution to the system of equations is x = 3 and y = -4, or (3,-4).