Put the steps in order that are used to solve the following systems of equations by subollution.
- 7x - 2y = - 13
x - 2y = 11
(10 points)
x - 2y = 11 -> x = 2y + 11
- 7(2y + 11) - 2y = - 13
- 14y - 77 - 2y = - 13
- 16y - 77 = - 13
x - 2(- 4) = 11
x + 8 = 11
- 16y = 64
x = 3
y = - 4
(3, - 4)
1) Rewrite the second equation in terms of x: x = 2y + 11
2) Substitute the value of x from step 1 into the first equation: -7(2y + 11) - 2y = -13
3) Simplify the equation: -14y - 77 - 2y = -13
4) Combine like terms: -16y - 77 = -13
5) Simplify further: -16y = 64
6) Solve for y: y = -4
7) Substitute the value of y from step 6 into the equation in step 1 to solve for x: x - 2(-4) = 11
8) Simplify the equation: x + 8 = 11
9) Solve for x: x = 3
10) The solution to the system of equations is (3, -4)
To solve the system of equations by substitution, here are the steps in order:
1. Solve one of the equations for one variable in terms of the other variable.
- In this case, solve the second equation for x: x = 2y + 11.
2. Substitute the expression for the variable into the other equation.
- Substitute x = 2y + 11 into the first equation: -7(2y + 11) - 2y = -13.
3. Simplify and solve the resulting equation to find the value of the second variable.
- Simplify the equation step by step: -14y - 77 - 2y = -13 -> -16y - 77 = -13.
- Solve for y: -16y = 64 -> y = -4.
4. Substitute the value of the second variable back into the equation from step 1 to find the value of the first variable.
- Substitute y = -4 into x = 2y + 11: x = 2(-4) + 11 -> x = 3.
5. Write the solution as an ordered pair (x, y).
- The solution is (3, -4).
To solve the system of equations by substitution, follow these steps:
1. Solve one equation for one variable in terms of the other variable.
- In this case, we can solve the equation x - 2y = 11 for x: x = 2y + 11.
2. Substitute the expression from step 1 into the other equation.
- Replace all instances of x in the second equation with the expression 2y + 11:
- 7(2y + 11) - 2y = -13.
3. Simplify and solve for the remaining variable.
- Distribute the 7 on the left side: 14y + 77 - 2y = -13.
- Combine like terms: 12y + 77 = -13.
- Subtract 77 from both sides: 12y = -90.
- Divide both sides by 12: y = -90/12 = -7.5.
4. Substitute the value of y back into the expression obtained in step 1 to find the corresponding x value.
- Replace y with -7.5 in the expression x = 2y + 11:
- x = 2(-7.5) + 11.
- Compute the result: x = -15 + 11 = -4.
5. State the solution as an ordered pair (x, y).
- The solution to the system of equations is (x, y) = (-4, -7.5).