Answer :
[tex]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=-\frac{3}{6}=-\frac{1}{2} \\ \\
\hbox{solve one of the equations for x:} \\
x=-2 \cdot (-\frac{1}{2}) +2=1+2=3 \\ \\ \hbox{the answer:} \\ x=3 \\ y=-\frac{1}{2}[/tex]
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
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
