Precalculus Examples

$3 x + 2 y = 4$ , $2 x + y = 1$ , $(- 2, - 5)$

Step 1

Simplify $3 (- 2) + 2 (- 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $3$ by $- 2$ .

$- 6 + 2 (- 5) = 4$

$2 (- 2) - 5 = 1$

Step 1.1.2

Multiply $2$ by $- 5$ .

$- 6 - 10 = 4$

$2 (- 2) - 5 = 1$

$- 6 - 10 = 4$

$2 (- 2) - 5 = 1$

Step 1.2

Subtract $10$ from $- 6$ .

$- 16 = 4$

$2 (- 2) - 5 = 1$

$- 16 = 4$

$2 (- 2) - 5 = 1$

Step 2

Since $- 16 \neq 4$ , there are no solutions.

No solution

Step 3

Simplify $2 (- 2) - 5$ .

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Step 3.1

Multiply $2$ by $- 2$ .

$- 4 - 5 = 1$

No solution

Step 3.2

Subtract $5$ from $- 4$ .

$- 9 = 1$

No solution

Step 4

Since $- 9 \neq 1$ , there are no solutions.

No solution

Step 5

The ordered pair is not a solution to the system of equations.

$(- 2, - 5)$ is not a solution