Put the steps in order that are used to solve the following systems of equations by substitution.
-72-24= -13
x-2y = 11
-16y = 64
= x-2y = 11 --> x = 2y + 11
-14y - 77 - 2y = - 13
-7(2y + 11) - 2y = - 13
(3, -4)
-16у - 77 = -13
x + 8 = 11
y = -4
x = 3
x - 2 (-4) = 11
Put the steps above in the right order, only use the numbers I listed above
1. x - 2y = 11
2. x = 2y + 11
3. Substitute x = 2y + 11 into the first equation
4. -14y - 77 - 2y = -13
5. -16y - 77 = -13
6. Solve for y
7. -16y = 64
8. y = -4
9. Substitute y = -4 into x = 2y + 11
10. x = 2(-4) + 11
11. x = 3
12. Solution: (x, y) = (3, -4)
To solve the system of equations by substitution, follow these steps in the correct order:
1. Start with the equation "x - 2y = 11".
2. Solve this equation for x by isolating the x term: "x = 2y + 11".
3. Substitute the value of x from step 2 into the other equation.
4. Replace x with the expression "2y + 11" in the second equation: "-16y - 77 = -13".
5. Simplify the equation from step 4: "-16y - 77 = -13".
6. Solve this equation for y: "-16y = -13 + 77" which gives "-16y = 64".
7. Divide both sides of the equation by -16 to solve for y: "y = 64 / -16".
8. Calculate y from step 7: "y = -4".
9. Substitute the value of y from step 8 into the equation from step 2: "x = 2(-4) + 11".
10. Simplify the equation from step 9: "x = -8 + 11".
11. Calculate x from step 10: "x = 3".
12. The solution to the system of equations is (x, y) = (3, -4).
That’s not right, there should only be 10 steps with the numbers I listed only
Apologies for the confusion. Here are the corrected steps in the order you provided:
1. -14y - 77 - 2y = -13
2. -16y - 77 = -13
3. Solve for y: -16y = 64
4. y = -4
5. Substitute y = -4 into the first equation
6. x - 2(-4) = 11
7. x + 8 = 11
8. Solve for x: x = 3
9. Solution: (x, y) = (3, -4)
10. -16y = -13 - 77
Step 5 and 10 are wrong
Apologies for the mistake. Here are the corrected steps:
1. x - 2y = 11
2. x = 2y + 11
3. Substitute x = 2y + 11 into the first equation: (2y + 11) - 2y = 11
4. 11 = 11
5. The two equations are dependent, which means there are infinitely many solutions.
6. There is no unique solution for this system of equations.
To solve the system of equations by substitution, follow these steps in the order provided:
1. Solve one equation for one variable (x or y) in terms of the other variable.
- From the equation x - 2y = 11, solve for x: x = 2y + 11
2. Substitute the expression for the solved variable in the other equation.
- Replace x in the equation -16y = 64 with the expression 2y + 11: -16(2y + 11) = 64
3. Simplify and solve the resulting equation.
- Simplify the expression: -32y - 176 = 64
- Combine like terms: -32y = 240
- Divide both sides by -32 to find the value of y: y = -240/32 = -7.5
4. Substitute the solved value of y back into one of the original equations to find the value of the remaining variable.
- Substitute y = -7.5 into the equation x - 2y = 11: x - 2(-7.5) = 11
- Simplify: x + 15 = 11
- Subtract 15 from both sides to find the value of x: x = 11 - 15 = -4
5. Write the solution as an ordered pair (x, y).
- The solution is (-4, -7.5), which can be written as (-4, -15/2) or approximately (-4, -7.5).