Solve by Substitution x-y=3 , x+3y=6

$x - y = 3$ , $x + 3 y = 6$

Step 1

Add $y$ to both sides of the equation.

$x = 3 + y$

$x + 3 y = 6$

Step 2

Replace all occurrences of $x$ with $3 + y$ in each equation.

Replace all occurrences of $x$ in $x + 3 y = 6$ with $3 + y$ .

$(3 + y) + 3 y = 6$

$x = 3 + y$

Simplify the left side.

Add $y$ and $3 y$ .

$3 + 4 y = 6$

$x = 3 + y$

$3 + 4 y = 6$

$x = 3 + y$

$3 + 4 y = 6$

$x = 3 + y$

Step 3

Solve for $y$ in $3 + 4 y = 6$ .

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

Subtract $3$ from both sides of the equation.

$4 y = 6 - 3$

$x = 3 + y$

Subtract $3$ from $6$ .

$4 y = 3$

$x = 3 + y$

$4 y = 3$

$x = 3 + y$

Divide each term in $4 y = 3$ by $4$ and simplify.

Divide each term in $4 y = 3$ by $4$ .

$\frac{4 y}{4} = \frac{3}{4}$

$x = 3 + y$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{3}{4}$

$x = 3 + y$

Divide $y$ by $1$ .

$y = \frac{3}{4}$

$x = 3 + y$

$y = \frac{3}{4}$

$x = 3 + y$

$y = \frac{3}{4}$

$x = 3 + y$

$y = \frac{3}{4}$

$x = 3 + y$

$y = \frac{3}{4}$

$x = 3 + y$

Step 4

Replace all occurrences of $y$ with $\frac{3}{4}$ in each equation.

Replace all occurrences of $y$ in $x = 3 + y$ with $\frac{3}{4}$ .

$x = 3 + \frac{3}{4}$

$y = \frac{3}{4}$

Simplify $x = 3 + \frac{3}{4}$ .

Simplify the left side.

Remove parentheses.

$x = 3 + \frac{3}{4}$

$y = \frac{3}{4}$

$x = 3 + \frac{3}{4}$

$y = \frac{3}{4}$

Simplify the right side.

Simplify $3 + \frac{3}{4}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = 3 \cdot \frac{4}{4} + \frac{3}{4}$

$y = \frac{3}{4}$

Combine $3$ and $\frac{4}{4}$ .

$x = \frac{3 \cdot 4}{4} + \frac{3}{4}$

$y = \frac{3}{4}$

Combine the numerators over the common denominator.

$x = \frac{3 \cdot 4 + 3}{4}$

$y = \frac{3}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$x = \frac{12 + 3}{4}$

$y = \frac{3}{4}$

Add $12$ and $3$ .

$x = \frac{15}{4}$

$y = \frac{3}{4}$

$x = \frac{15}{4}$

$y = \frac{3}{4}$

$x = \frac{15}{4}$

$y = \frac{3}{4}$

$x = \frac{15}{4}$

$y = \frac{3}{4}$

$x = \frac{15}{4}$

$y = \frac{3}{4}$

$x = \frac{15}{4}$

$y = \frac{3}{4}$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{15}{4}, \frac{3}{4})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{15}{4}, \frac{3}{4})$

Equation Form:

$x = \frac{15}{4}, y = \frac{3}{4}$

Step 7

Solve by Substitution x-y=3 , x+3y=6

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