How do you solve $x + y = 10$ and $x - y = 8$ ?

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Answer 1 · 2015-08-06T09:36:01

${(x = 9), (y=1) :}$

The easiest way in which you can solve this system of equations is to add the two equations to get the value of $x$ .

More specifically, you add the left side of the equations and the right side of the equations separately.

${(x+y = 10), (x-y = 8) :}$

$x + color(red)cancelcolor(black)(y) + x - color(red)cancelcolor(black)(y) = 10 + 8$

$2x = 18 implies x= 18/2 = color(green)(9)$

Now use the value of $x$ in one of the two equations to get the value of $y$

$9 + y = 10 implies y = 10 - 9 = color(green)(1)$

How do you solve x + y = 10 x + y = 10 and x - y = 8x - y = 8?