Finite Math Examples

$y - x = 3$ , $x - y = 2$

Step 1

Add $x$ to both sides of the equation.

$y = 3 + x$

$x - y = 2$

Step 2

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

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Step 2.1

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

$x - (3 + x) = 2$

$y = 3 + x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x - (3 + x)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$x - 1 \cdot 3 - x = 2$

$y = 3 + x$

Step 2.2.1.1.2

Multiply $- 1$ by $3$ .

$x - 3 - x = 2$

$y = 3 + x$

$x - 3 - x = 2$

$y = 3 + x$

Step 2.2.1.2

Combine the opposite terms in $x - 3 - x$ .

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Step 2.2.1.2.1

Subtract $x$ from $x$ .

$0 - 3 = 2$

$y = 3 + x$

Step 2.2.1.2.2

Subtract $3$ from $0$ .

$- 3 = 2$

$y = 3 + x$

$- 3 = 2$

$y = 3 + x$

$- 3 = 2$

$y = 3 + x$

$- 3 = 2$

$y = 3 + x$

$- 3 = 2$

$y = 3 + x$

Step 3

Since $- 3 = 2$ is not true, there is no solution.

No solution

Step 4