Finite Math Examples

$x + y = 130$ , $20 x + 10 y = 1500$ , $x = 45$ , $y = 32$

Step 1

Replace all occurrences of $x$ with $45$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $x + y = 130$ with $45$ .

$(45) + y = 130$

$x = 45$

$20 x + 10 y = 1500$

$y = 32$

Step 1.2

Simplify the left side.

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Step 1.2.1

Remove parentheses.

$45 + y = 130$

$x = 45$

$20 x + 10 y = 1500$

$y = 32$

$45 + y = 130$

$x = 45$

$20 x + 10 y = 1500$

$y = 32$

Step 1.3

Replace all occurrences of $x$ in $20 x + 10 y = 1500$ with $45$ .

$20 (45) + 10 y = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

Step 1.4

Simplify the left side.

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Step 1.4.1

Multiply $20$ by $45$ .

$900 + 10 y = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

$900 + 10 y = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

$900 + 10 y = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

Step 2

Replace all occurrences of $y$ with $32$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $900 + 10 y = 1500$ with $32$ .

$900 + 10 (32) = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $900 + 10 (32)$ .

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Step 2.2.1.1

Multiply $10$ by $32$ .

$900 + 320 = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

Step 2.2.1.2

Add $900$ and $320$ .

$1220 = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

$1220 = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

$1220 = 1500$

$45 + y = 130$

$x = 45$

$y = 32$

Step 2.3

Replace all occurrences of $y$ in $45 + y = 130$ with $32$ .

$45 + 32 = 130$

$1220 = 1500$

$x = 45$

$y = 32$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $45 + 32$ .

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Step 2.4.1.1

Remove parentheses.

$45 + 32 = 130$

$1220 = 1500$

$x = 45$

$y = 32$

Step 2.4.1.2

Add $45$ and $32$ .

$77 = 130$

$1220 = 1500$

$x = 45$

$y = 32$

$77 = 130$

$1220 = 1500$

$x = 45$

$y = 32$

$77 = 130$

$1220 = 1500$

$x = 45$

$y = 32$

$77 = 130$

$1220 = 1500$

$x = 45$

$y = 32$

Step 3

Since $77 = 130$ is not true, there is no solution.

No solution

Step 4