Finite Math Examples

$3 y - 2 x = 0$ , $y + 8 x = 52$ , $y - 2 x = 2$ , $x = 3$

Step 1

Replace all occurrences of $x$ with $3$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $3 y - 2 x = 0$ with $3$ .

$3 y - 2 \cdot 3 = 0$

$x = 3$

$y + 8 x = 52$

$y - 2 x = 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $- 2$ by $3$ .

$3 y - 6 = 0$

$x = 3$

$y + 8 x = 52$

$y - 2 x = 2$

$3 y - 6 = 0$

$x = 3$

$y + 8 x = 52$

$y - 2 x = 2$

Step 1.3

Replace all occurrences of $x$ in $y + 8 x = 52$ with $3$ .

$y + 8 (3) = 52$

$3 y - 6 = 0$

$x = 3$

$y - 2 x = 2$

Step 1.4

Simplify the left side.

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Step 1.4.1

Multiply $8$ by $3$ .

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

$y - 2 x = 2$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

$y - 2 x = 2$

Step 1.5

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

$y - 2 \cdot 3 = 2$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

Step 1.6

Simplify the left side.

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Step 1.6.1

Multiply $- 2$ by $3$ .

$y - 6 = 2$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

$y - 6 = 2$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

$y - 6 = 2$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $6$ to both sides of the equation.

$y = 2 + 6$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

Step 2.2

Add $2$ and $6$ .

$y = 8$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

$y = 8$

$y + 24 = 52$

$3 y - 6 = 0$

$x = 3$

Step 3

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

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Step 3.1

Replace all occurrences of $y$ in $y + 24 = 52$ with $8$ .

$(8) + 24 = 52$

$y = 8$

$3 y - 6 = 0$

$x = 3$

Step 3.2

Simplify the left side.

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Step 3.2.1

Add $8$ and $24$ .

$32 = 52$

$y = 8$

$3 y - 6 = 0$

$x = 3$

$32 = 52$

$y = 8$

$3 y - 6 = 0$

$x = 3$

Step 3.3

Replace all occurrences of $y$ in $3 y - 6 = 0$ with $8$ .

$3 (8) - 6 = 0$

$32 = 52$

$y = 8$

$x = 3$

Step 3.4

Simplify the left side.

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Step 3.4.1

Simplify $3 (8) - 6$ .

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Step 3.4.1.1

Multiply $3$ by $8$ .

$24 - 6 = 0$

$32 = 52$

$y = 8$

$x = 3$

Step 3.4.1.2

Subtract $6$ from $24$ .

$18 = 0$

$32 = 52$

$y = 8$

$x = 3$

$18 = 0$

$32 = 52$

$y = 8$

$x = 3$

$18 = 0$

$32 = 52$

$y = 8$

$x = 3$

$18 = 0$

$32 = 52$

$y = 8$

$x = 3$

Step 4

Since $18 = 0$ is not true, there is no solution.

No solution

Step 5