Finite Math Examples

$y = - 3 x + 7$ , $6 x + 2 y = 13$

Step 1

Replace all occurrences of $y$ with $- 3 x + 7$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $6 x + 2 y = 13$ with $- 3 x + 7$ .

$6 x + 2 (- 3 x + 7) = 13$

$y = - 3 x + 7$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $6 x + 2 (- 3 x + 7)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$6 x + 2 (- 3 x) + 2 \cdot 7 = 13$

$y = - 3 x + 7$

Step 1.2.1.1.2

Multiply $- 3$ by $2$ .

$6 x - 6 x + 2 \cdot 7 = 13$

$y = - 3 x + 7$

Step 1.2.1.1.3

Multiply $2$ by $7$ .

$6 x - 6 x + 14 = 13$

$y = - 3 x + 7$

$6 x - 6 x + 14 = 13$

$y = - 3 x + 7$

Step 1.2.1.2

Simplify by adding terms.

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Step 1.2.1.2.1

Subtract $6 x$ from $6 x$ .

$0 + 14 = 13$

$y = - 3 x + 7$

Step 1.2.1.2.2

Add $0$ and $14$ .

$14 = 13$

$y = - 3 x + 7$

$14 = 13$

$y = - 3 x + 7$

$14 = 13$

$y = - 3 x + 7$

$14 = 13$

$y = - 3 x + 7$

$14 = 13$

$y = - 3 x + 7$

Step 2

Since $14 = 13$ is not true, there is no solution.

No solution

Step 3