How do you solve x + y = 5 and 2x + Y = 8?

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Answer 1 · 2016-01-08T04:47:42

$(3,2)$

This could be solved with either elimination or substitution. I'll use elimination, since the category is "Linear Systems with Multiplication."

Multiply the first equation by $-1$ .

$-1(x+y=5)rarr-x-y=-5$

We now have the two equations:

${(-x-y=-5),(2x+y=8):}$

Add the two equations together.

$-x+2x-y+y=-5+8$

Simplify. Notice that the $y$ terms cancel, which was the point in multiplying the first equation by $-1$ earlier.

$x=3$

Now, substitute $x=3$ into either of the original equations.

$3+y=5$
$y=2$

This leaves us with $x=3,y=2$ , or the point $(3,2)$ .