Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13
x−2y = 11 are the equations don't give me steps in words just put the numbers in order give me 10 steps
x - 2y = 11 --> x = 2y + 11
-16y = 64
-16y - 77 = -13
x - 2(-4) = 11
x + 8 = 11
y = -4
x = 3
-14y - 77 -2y = -13
-7 (2y + 11) -2y = -13
(3, -4)
1. Rewrite one of the equations in terms of one variable (x or y).
2. Solve for one variable in terms of the other.
3. Substitute the expression from step 2 into the other equation.
4. Simplify the equation after substitution.
5. Solve for the remaining variable.
6. Substitute the value found in step 5 back into one of the original equations.
7. Simplify the equation after substitution.
8. Solve for the remaining variable.
9. Check the solution by substituting the values back into both original equations.
10. Write the solution as an ordered pair (x, y).
1. Start with the system of equations:
-7x - 2y = -13
x - 2y = 11
2. Solve one equation for one variable:
x - 2y = 11 --> x = 2y + 11
3. Substitute the expression for x into the other equation:
-7(2y + 11) - 2y = -13
4. Simplify and solve for y:
-16y - 77 -2y = -13
-14y - 77 = -13
-14y = 64
y = -4
5. Substitute the value of y back into the expression for x:
x = 2(-4) + 11
x = 3
6. The solution is the values of x and y:
(x, y) = (3, -4)
Alternatively:
1. Start with the system of equations:
-7x - 2y = -13
x - 2y = 11
2. Solve one equation for one variable:
x - 2y = 11 --> x = 2y + 11
3. Substitute the expression for x into the other equation:
-7(2y + 11) - 2y = -13
4. Simplify and solve for y:
-16y - 77 - 2y = -13
-16y - 2y - 77 = -13
-18y - 77 = -13
-18y = 64
y = -4
5. Substitute the value of y back into the expression for x:
x = 2(-4) + 11
x = 3
6. The solution is the values of x and y:
(x, y) = (3, -4)
1. Rewrite one equation in terms of one variable (solve for x or y).
2. Rewrite the other equation in terms of the same variable.
3. Set the two equations equal to each other: equation 1 = equation 2.
4. Solve the new equation for the variable.
5. Substitute the value of the variable found in step 4 into one of the original equations.
6. Solve for the other variable.
7. Substitute the value of the second variable back into one of the original equations to find the value of the first variable.
8. Check the solution by plugging the values of the variables back into both original equations to see if they are satisfied.
9. Write the solution as an ordered pair (x, y).
10. Simplify or evaluate any additional expressions, if necessary.
So, the correct order of the steps is:
1. x - 2y = 11 --> x = 2y + 11
2. -16y - 77 = -13
3. -16y = 64
4. x - 2(-4) = 11
5. x + 8 = 11
6. y = -4
7. x = 3
8. -14y - 77 - 2y = -13 (substituting the value of x into the other equation)
9. -7(2y + 11) - 2y = -13
10. Solution: (3, -4)