Algebra Examples

$2 r - t = 7$ $r - t = 1$

Step 1

Add $t$ to both sides of the equation.

$r = 1 + t$

$2 r - t = 7$

Step 2

Replace all occurrences of $r$ with $1 + t$ in each equation.

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Step 2.1

Replace all occurrences of $r$ in $2 r - t = 7$ with $1 + t$ .

$2 (1 + t) - t = 7$

$r = 1 + t$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (1 + t) - t$ .

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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.

$2 \cdot 1 + 2 t - t = 7$

$r = 1 + t$

Step 2.2.1.1.2

Multiply $2$ by $1$ .

$2 + 2 t - t = 7$

$r = 1 + t$

$2 + 2 t - t = 7$

$r = 1 + t$

Step 2.2.1.2

Subtract $t$ from $2 t$ .

$2 + t = 7$

$r = 1 + t$

$2 + t = 7$

$r = 1 + t$

$2 + t = 7$

$r = 1 + t$

$2 + t = 7$

$r = 1 + t$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$t = 7 - 2$

$r = 1 + t$

Step 3.2

Subtract $2$ from $7$ .

$t = 5$

$r = 1 + t$

$t = 5$

$r = 1 + t$

Step 4

Replace all occurrences of $t$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $t$ in $r = 1 + t$ with $5$ .

$r = 1 + 5$

$t = 5$

Step 4.2

Simplify $r = 1 + 5$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$r = 1 + 5$

$t = 5$

$r = 1 + 5$

$t = 5$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $1$ and $5$ .

$r = 6$

$t = 5$

$r = 6$

$t = 5$

$r = 6$

$t = 5$

$r = 6$

$t = 5$

Step 5

List all of the solutions.

$r = 6, t = 5$