Put the steps in order that are used to solve the following systems of equations by substitution.
−7x−2y=−13
x−2y=11
A. -14y - 77 - 2y = -13
B. -16y = 64
C. x = 3
D. x - 2y = 11 --> x = 2y + 11
E. -16y - 77 = -13
F. (3, -4)
G. x + 8 = 11
H. y = -4
I. x - 2 (-4) = 11
J. -7 (2y + 11) -2y = -13
1. Rearrange one equation to solve for one variable in terms of the other variable
-7x - 2y = -13 => x = (2y + 11)
2. Substitute the expression for the variable into the other equation
x - 2y = 11
=> (2y + 11) - 2y = 11
3. Simplify the equation
2y + 11 - 2y = 11
4. Solve for y
11 = 11
5. Determine the value of y
y = -4
6. Substitute the value of y back into the expression for x to find the value of x
x = 2(-4) + 11
7. Simplify the equation
x = 3
8. Determine the solution of the system of equations
(x, y) = (3, -4)
The correct order of steps is:
D. x - 2y = 11 --> x = 2y + 11
G. x + 8 = 11
J. -7 (2y + 11) -2y = -13
I. x - 2(-4) = 11
H. y = -4
F. (3, -4)
The correct order of steps to solve the system of equations by substitution is as follows:
1. Rearrange one of the equations to solve for one variable in terms of the other variable. In this case, rearrange the second equation, "x - 2y = 11," to get "x = 2y + 11."
2. Substitute the expression obtained in step 1 into the other equation. Replace the "x" in the first equation with "2y + 11." This will give us a new equation with only one variable.
3. Solve the resulting equation for the variable. Simplify and solve for the value of "y."
4. Substitute the value of "y" obtained in step 3 back into either of the original equations to solve for "x." In this case, substitute the value of "y" in "x = 2y + 11." Simplify and solve for the value of "x."
5. The solution to the system of equations is the values of "x" and "y" obtained in steps 3 and 4. Write the solution as an ordered pair (x, y).
Therefore, the correct order of steps is:
D. x - 2y = 11 --> x = 2y + 11
J. -7 (2y + 11) -2y = -13
E. -16y - 77 = -13
H. y = -4
I. x - 2 (-4) = 11
G. x + 8 = 11
C. x = 3
A. -14y - 77 - 2y = -13
B. -16y = 64
F. (3, -4)
To solve the given system of equations by substitution, follow these steps:
1. Start with the two equations:
-7x - 2y = -13 ----(Equation 1)
x - 2y = 11 ----(Equation 2)
2. Solve one of the equations for one variable in terms of the other variable. In this case, Equation 2 can be rearranged to get x in terms of y:
x = 2y + 11 ----(Equation 2 rearranged)
3. Substitute the expression for x from Equation 2 into Equation 1:
-7(2y + 11) - 2y = -13
4. Simplify the equation by distributing and combining like terms:
-14y - 77 - 2y = -13
5. Continue simplifying:
-16y - 77 = -13
6. Move all terms to one side of the equation by adding 77 to both sides:
-16y - 77 + 77 = -13 + 77
7. Simplify further to isolate the variable:
-16y = 64
8. Divide both sides of the equation by -16 to solve for y:
y = 64 / -16
9. Simplify the equation to find the value of y:
y = -4
10. Substitute the value of y back into Equation 2 to solve for x:
x = 2(-4) + 11
11. Simplify further to find the value of x:
x = 3
So, the solution to the system of equations is x = 3, y = -4, or (3, -4) in coordinate form.
The correct order of steps is:
B. -16y = 64
H. y = -4
D. x - 2y = 11 --> x = 2y + 11
C. x = 3
F. (3, -4)
J. -7 (2y + 11) - 2y = -13
E. -16y - 77 = -13
G. x + 8 = 11
A. -14y - 77 - 2y = -13
I. x - 2 (-4) = 11