Finite Math Examples

$7 x - y = 14$ , $3 x + y = 12$ , $x = 2$ , $y = 8$

Step 1

Replace all occurrences of $x$ with $2$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $7 x - y = 14$ with $2$ .

$7 (2) - y = 14$

$x = 2$

$3 x + y = 12$

$y = 8$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $7$ by $2$ .

$14 - y = 14$

$x = 2$

$3 x + y = 12$

$y = 8$

$14 - y = 14$

$x = 2$

$3 x + y = 12$

$y = 8$

Step 1.3

Replace all occurrences of $x$ in $3 x + y = 12$ with $2$ .

$3 (2) + y = 12$

$14 - y = 14$

$x = 2$

$y = 8$

Step 1.4

Simplify the left side.

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Step 1.4.1

Multiply $3$ by $2$ .

$6 + y = 12$

$14 - y = 14$

$x = 2$

$y = 8$

$6 + y = 12$

$14 - y = 14$

$x = 2$

$y = 8$

$6 + y = 12$

$14 - y = 14$

$x = 2$

$y = 8$

Step 2

Replace all occurrences of $y$ with $8$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $6 + y = 12$ with $8$ .

$6 + 8 = 12$

$14 - y = 14$

$x = 2$

$y = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $6 + 8$ .

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Step 2.2.1.1

Remove parentheses.

$6 + 8 = 12$

$14 - y = 14$

$x = 2$

$y = 8$

Step 2.2.1.2

Add $6$ and $8$ .

$14 = 12$

$14 - y = 14$

$x = 2$

$y = 8$

$14 = 12$

$14 - y = 14$

$x = 2$

$y = 8$

$14 = 12$

$14 - y = 14$

$x = 2$

$y = 8$

Step 2.3

Replace all occurrences of $y$ in $14 - y = 14$ with $8$ .

$14 - (8) = 14$

$14 = 12$

$x = 2$

$y = 8$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $14 - (8)$ .

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Step 2.4.1.1

Multiply $- 1$ by $8$ .

$14 - 8 = 14$

$14 = 12$

$x = 2$

$y = 8$

Step 2.4.1.2

Subtract $8$ from $14$ .

$6 = 14$

$14 = 12$

$x = 2$

$y = 8$

$6 = 14$

$14 = 12$

$x = 2$

$y = 8$

$6 = 14$

$14 = 12$

$x = 2$

$y = 8$

$6 = 14$

$14 = 12$

$x = 2$

$y = 8$

Step 3

Since $6 = 14$ is not true, there is no solution.

No solution

Step 4