Algebra Examples

$- r + t = 5$ $- 2 r + t = 4$

Step 1

Add $r$ to both sides of the equation.

$t = 5 + r$

$- 2 r + t = 4$

Step 2

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

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Step 2.1

Replace all occurrences of $t$ in $- 2 r + t = 4$ with $5 + r$ .

$- 2 r + 5 + r = 4$

$t = 5 + r$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 2 r + 5 + r$ .

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Step 2.2.1.1

Remove parentheses.

$- 2 r + 5 + r = 4$

$t = 5 + r$

Step 2.2.1.2

Add $- 2 r$ and $r$ .

$- r + 5 = 4$

$t = 5 + r$

$- r + 5 = 4$

$t = 5 + r$

$- r + 5 = 4$

$t = 5 + r$

$- r + 5 = 4$

$t = 5 + r$

Step 3

Solve for $r$ in $- r + 5 = 4$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5$ from both sides of the equation.

$- r = 4 - 5$

$t = 5 + r$

Step 3.1.2

Subtract $5$ from $4$ .

$- r = - 1$

$t = 5 + r$

$- r = - 1$

$t = 5 + r$

Step 3.2

Divide each term in $- r = - 1$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- r = - 1$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- 1}{- 1}$

$t = 5 + r$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- 1}{- 1}$

$t = 5 + r$

Step 3.2.2.2

Divide $r$ by $1$ .

$r = \frac{- 1}{- 1}$

$t = 5 + r$

$r = \frac{- 1}{- 1}$

$t = 5 + r$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 1$ by $- 1$ .

$r = 1$

$t = 5 + r$

$r = 1$

$t = 5 + r$

$r = 1$

$t = 5 + r$

$r = 1$

$t = 5 + r$

Step 4

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

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Step 4.1

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

$t = 5 + 1$

$r = 1$

Step 4.2

Simplify $t = 5 + 1$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$t = 5 + 1$

$r = 1$

$t = 5 + 1$

$r = 1$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $5$ and $1$ .

$t = 6$

$r = 1$

$t = 6$

$r = 1$

$t = 6$

$r = 1$

$t = 6$

$r = 1$

Step 5

List all of the solutions.

$t = 6, r = 1$