# A system of equations contains the lines x+4y=2 and x−2y=c. When solving the system algebraically, it is determined that x=6. What is the value of c in the second equation?

Apr 12, 2018

c=8

#### Explanation:

1. To solve this problem you must begin by substituting 6 for x.
6+4y=2 and 6-2y=c
2. Solve each for y.
y= $\frac{1}{2}$ - $\frac{3}{2}$ and y= $- \frac{c}{2}$ + 3
3. Set the equations equal to each other.
$\frac{1}{2}$ - $\frac{3}{2}$=$- \frac{c}{2}$ + 3
4. Multiply everything by 2 to cancel out the denominators.
1-3=-c+6
5. Simplify
-2=-c+6
6. Solve for c by subtracting 6 and dividing by -1.
c=8