Solve the System of Equations 56s=70t s=t+1/2

$56 s = 70 t$ $s = t + \frac{1}{2}$

Step 1

Replace all occurrences of $s$ with $t + \frac{1}{2}$ in each equation.

Replace all occurrences of $s$ in $56 s = 70 t$ with $t + \frac{1}{2}$ .

$56 (t + \frac{1}{2}) = 70 t$

$s = t + \frac{1}{2}$

Simplify the left side.

Simplify $56 (t + \frac{1}{2})$ .

Apply the distributive property.

$56 t + 56 (\frac{1}{2}) = 70 t$

$s = t + \frac{1}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $56$ .

$56 t + 2 (28) (\frac{1}{2}) = 70 t$

$s = t + \frac{1}{2}$

Cancel the common factor.

$56 t + 2 \cdot (28 (\frac{1}{2})) = 70 t$

$s = t + \frac{1}{2}$

Rewrite the expression.

$56 t + 28 = 70 t$

$s = t + \frac{1}{2}$

$56 t + 28 = 70 t$

$s = t + \frac{1}{2}$

$56 t + 28 = 70 t$

$s = t + \frac{1}{2}$

$56 t + 28 = 70 t$

$s = t + \frac{1}{2}$

$56 t + 28 = 70 t$

$s = t + \frac{1}{2}$

Step 2

Solve for $t$ in $56 t + 28 = 70 t$ .

Move all terms containing $t$ to the left side of the equation.

Subtract $70 t$ from both sides of the equation.

$56 t + 28 - 70 t = 0$

$s = t + \frac{1}{2}$

Subtract $70 t$ from $56 t$ .

$- 14 t + 28 = 0$

$s = t + \frac{1}{2}$

$- 14 t + 28 = 0$

$s = t + \frac{1}{2}$

Subtract $28$ from both sides of the equation.

$- 14 t = - 28$

$s = t + \frac{1}{2}$

Divide each term in $- 14 t = - 28$ by $- 14$ and simplify.

Divide each term in $- 14 t = - 28$ by $- 14$ .

$\frac{- 14 t}{- 14} = \frac{- 28}{- 14}$

$s = t + \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 t}{- 14} = \frac{- 28}{- 14}$

$s = t + \frac{1}{2}$

Divide $t$ by $1$ .

$t = \frac{- 28}{- 14}$

$s = t + \frac{1}{2}$

$t = \frac{- 28}{- 14}$

$s = t + \frac{1}{2}$

$t = \frac{- 28}{- 14}$

$s = t + \frac{1}{2}$

Simplify the right side.

Divide $- 28$ by $- 14$ .

$t = 2$

$s = t + \frac{1}{2}$

$t = 2$

$s = t + \frac{1}{2}$

$t = 2$

$s = t + \frac{1}{2}$

$t = 2$

$s = t + \frac{1}{2}$

Step 3

Replace all occurrences of $t$ with $2$ in each equation.

Replace all occurrences of $t$ in $s = t + \frac{1}{2}$ with $2$ .

$s = (2) + \frac{1}{2}$

$t = 2$

Simplify the right side.

Simplify $(2) + \frac{1}{2}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$s = 2 \cdot \frac{2}{2} + \frac{1}{2}$

$t = 2$

Combine $2$ and $\frac{2}{2}$ .

$s = \frac{2 \cdot 2}{2} + \frac{1}{2}$

$t = 2$

Combine the numerators over the common denominator.

$s = \frac{2 \cdot 2 + 1}{2}$

$t = 2$

Simplify the numerator.

Multiply $2$ by $2$ .

$s = \frac{4 + 1}{2}$

$t = 2$

Add $4$ and $1$ .

$s = \frac{5}{2}$

$t = 2$

$s = \frac{5}{2}$

$t = 2$

$s = \frac{5}{2}$

$t = 2$

$s = \frac{5}{2}$

$t = 2$

$s = \frac{5}{2}$

$t = 2$

Step 4

List all of the solutions.

$s = \frac{5}{2}, t = 2$

Solve the System of Equations 56s=70t s=t+1/2

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