Answer:
x=10
Step-by-step explanation:
We have the system [tex]\left \{ {{x+4y=18} \atop {x-4y=2}} \right.[/tex] and we have to find the value of x,
we can clear y from both equations and then match them.
First equation:
[tex]x+4y=18\\4y=18-x\\y=\frac{18-x}{4}[/tex]
Second equation:
[tex]x-4y=2\\4y=x-2\\y=\frac{x-2}{4}[/tex]
Now matching both equations:
[tex]y=y\\\frac{18-x}{4}=\frac{x-2}{4}\\18-x=x-2[/tex]
We can subtract x in both sides,
[tex]18-x=x-2\\18-x-x=x-2-x\\18-2x=-2[/tex]
Subtract 18 in both sides,
[tex]18-2x=-2\\18-2x-18=-2-18\\-2x=-20[/tex]
Divide both sides in (-2),
[tex]-2x=-20\\\frac{-2x}{-2} =\frac{-20}{-2}\\ x=10[/tex]
Result: x=10
