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Is the ordered pair (2,2) a solution to the system 2x - y = 2 and x + 3y =8?

1 Answer

May 10, 2016

Yes; $(x, y) = (2, 2)$ $(x,y)=(2,2)$ is a solution to
$XXX 2 x - y = 2$ $color(white)("XXX")2x-y=2$ and
$XXX x + 3 y = 8$ $color(white)("XXX")x+3y=8$

Explanation:

Substituting $(2, 2)$ $(color(red)(2),color(blue)(2))$ for $(x, y)$ $(color(red)(x),color(blue)(y))$

in the expression $2 x - y$ $2color(red)(x)-color(blue)(y)$
gives $(2 \times 2) + 2 = 2$ $(2xxcolor(red)(2))+color(blue)(2) = 2$
So $(2, 2)$ $(color(red)(2),color(blue)(2))$ is a solution for $2 x - y = 2$ $2color(red)(x)-color(blue)(y)=2$
in the expression $x + 3 x$ $color(red)(x)+3color(blue)(x)$
gives $2 + (3 \times 2) = 8$ $color(red)(2)+(3xxcolor(blue)(2))=8$
So $(2, 2)$ $(color(red)(2),color(blue)(2))$ is a solution for $x + 3 y = 8$ $color(red)(x)+3color(blue)(y)=8$

Since $(2, 2)$ $(color(red)(2),color(blue)(2))$ is a solution for both equations,
it is a solution for the system of equations (since the system is comprised of only those two equations).

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