Is $(2, 5)$ $(2,5)$ a solution to the system of equations $6 x + y = 17$ $6x + y = 17$ and $3 x + 2 y = 16$ $3x + 2y = 16$ ?

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Answer 1 · 2017-03-04T17:59:37

Because the pair is a solution for both equations it is therefore a solution for the system of equations.

First, substitute $2$ $2$ for $x$ $x$ and $5$ $5$ for $y$ $y$ in the first equation and determine if this pair is a solution:

$6 x + y = 17$ $6x + y = 17$ becomes:

$(6 \times 2) + 5 = 17$ $(6 xx 2) + 5 = 17$

$12 + 5 = 17$ $12 + 5 = 17$

$17 = 17$ $17 = 17$

Because the pair is a solution for the first equation we must do the same substitution and solution for the second equation:

$3 x + 2 y = 16$ $3x + 2y = 16$ becomes:

$(3 \times 2) + (2 \times 5) = 16$ $(3 xx 2) + (2 xx 5) = 16$

$6 + 10 = 16$ $6 + 10 = 16$

$16 = 16$ $16 = 16$

Is (2,5)(2,5) a solution to the system of equations 6x+y=176x + y = 17 and 3x+2y=163x + 2y = 16?