Solve the System of Equations 3a+b=225 b-a=25

$3 a + b = 225$ $b - a = 25$

Step 1

Subtract $3 a$ from both sides of the equation.

$b = 225 - 3 a$

$b - a = 25$

Step 2

Replace all occurrences of $b$ with $225 - 3 a$ in each equation.

Replace all occurrences of $b$ in $b - a = 25$ with $225 - 3 a$ .

$(225 - 3 a) - a = 25$

$b = 225 - 3 a$

Simplify the left side.

Subtract $a$ from $- 3 a$ .

$225 - 4 a = 25$

$b = 225 - 3 a$

$225 - 4 a = 25$

$b = 225 - 3 a$

$225 - 4 a = 25$

$b = 225 - 3 a$

Step 3

Solve for $a$ in $225 - 4 a = 25$ .

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

Subtract $225$ from both sides of the equation.

$- 4 a = 25 - 225$

$b = 225 - 3 a$

Subtract $225$ from $25$ .

$- 4 a = - 200$

$b = 225 - 3 a$

$- 4 a = - 200$

$b = 225 - 3 a$

Divide each term in $- 4 a = - 200$ by $- 4$ and simplify.

Divide each term in $- 4 a = - 200$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{- 200}{- 4}$

$b = 225 - 3 a$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{- 200}{- 4}$

$b = 225 - 3 a$

Divide $a$ by $1$ .

$a = \frac{- 200}{- 4}$

$b = 225 - 3 a$

$a = \frac{- 200}{- 4}$

$b = 225 - 3 a$

$a = \frac{- 200}{- 4}$

$b = 225 - 3 a$

Simplify the right side.

Divide $- 200$ by $- 4$ .

$a = 50$

$b = 225 - 3 a$

$a = 50$

$b = 225 - 3 a$

$a = 50$

$b = 225 - 3 a$

$a = 50$

$b = 225 - 3 a$

Step 4

Replace all occurrences of $a$ with $50$ in each equation.

Replace all occurrences of $a$ in $b = 225 - 3 a$ with $50$ .

$b = 225 - 3 \cdot 50$

$a = 50$

Simplify the right side.

Simplify $225 - 3 \cdot 50$ .

Multiply $- 3$ by $50$ .

$b = 225 - 150$

$a = 50$

Subtract $150$ from $225$ .

$b = 75$

$a = 50$

$b = 75$

$a = 50$

$b = 75$

$a = 50$

$b = 75$

$a = 50$

Step 5

List all of the solutions.

$b = 75, a = 50$

Solve the System of Equations 3a+b=225 b-a=25

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