Question

Solve, using the substitution method.

4x + 2y = 11
x – 2 = – 2y


A.


B.


C.


D.

Answer 1

4x + 2y = 11
x - 2 = -2y
First you have to get a variable alone in one of the equations.

x - 2 = -2y
+2 +2
--------------
x = -2y + 2
Next you substitute -2y +2 for x in the second equation.

4(-2y + 2) + 2y = 11
Distribute.

-8y + 8 + 2y = 11
Combine like terms.

-6y + 8 = 11
Get the variable (y) by itself.

-6y + 8 = 11
-8 -8
--------------------
-6y = 3
Finally get y by itself.

-6y = 3
----- ------
-6 -6

Y = 0.5

Now to get x you plugin the answer for y.

x - 2 = -2y
x - 2 = -2(0.5)
x - 2 = -1
+2 +2
x = 1

(1, 0.5) Is your ordered pair. :D

Answer 2

`4x+2y=11 \\ x-2=-2y \\ \\ \hbox{from the 2nd equation:} \\ x-2=-2y \\ x=-2y+2 \\ \\ \hbox{substitute -2y+2 for x in the 1st equation:} \\ 4(-2y+2)+2y=11 \\ -8y+8+2y=11 \\ -8y+2y=11-8 \\ -6y=3 \\ y=-(3)/(6)=-(1)/(2) \\ \\ \hbox{solve one of the equations for x:} \\ x=-2 \cdot (-(1)/(2)) +2=1+2=3 \\ \\ \hbox{the answer:} \\ x=3 \\ y=-(1)/(2)`