Precalculus Examples

$y = 5 x + 2$ , $2 y = 2 x + 12$ , $(1, 7)$

Rewrite the equation as $5 (1) + 2 = 7$ .

$5 (1) + 2 = 7$

$2 (7) = 2 (1) + 12$

Multiply $5$ by $1$ to get $5$ .

$5 + 2 = 7$

$2 (7) = 2 (1) + 12$

Add $5$ and $2$ to get $7$ .

$7 = 7$

$2 (7) = 2 (1) + 12$

Since $7 = 7$ , the equation will always be true.

Always true

$2 (7) = 2 (1) + 12$

Rewrite the equation as $2 (1) + 12 = 2 (7)$ .

$A l w a y s (t r u e)$

$2 (1) + 12 = 2 (7)$

Multiply $2$ by $1$ to get $2$ .

$A l w a y s (t r u e)$

$2 + 12 = 2 (7)$

Add $2$ and $12$ to get $14$ .

$A l w a y s (t r u e)$

$14 = 2 (7)$

Multiply $2$ by $7$ to get $14$ .

$A l w a y s (t r u e)$

$14 = 14$

Since $14 = 14$ , the equation will always be true.

$A l w a y s (t r u e)$

Always true

The ordered pair is a solution to the system of equations.

$(1, 7)$ is a solution

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