Solve the System of Equations x=y-3 x/2+2y=6

$x = y - 3$ $\frac{x}{2} + 2 y = 6$

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

Replace all occurrences of $x$ in $\frac{x}{2} + 2 y = 6$ with $y - 3$ .

$\frac{y - 3}{2} + 2 y = 6$

$x = y - 3$

Simplify the left side.

Simplify $\frac{y - 3}{2} + 2 y$ .

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

$\frac{y - 3}{2} + 2 y \cdot \frac{2}{2} = 6$

$x = y - 3$

Simplify terms.

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

$\frac{y - 3}{2} + \frac{2 y \cdot 2}{2} = 6$

$x = y - 3$

Combine the numerators over the common denominator.

$\frac{y - 3 + 2 y \cdot 2}{2} = 6$

$x = y - 3$

$\frac{y - 3 + 2 y \cdot 2}{2} = 6$

$x = y - 3$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{y - 3 + 4 y}{2} = 6$

$x = y - 3$

Add $y$ and $4 y$ .

$\frac{5 y - 3}{2} = 6$

$x = y - 3$

$\frac{5 y - 3}{2} = 6$

$x = y - 3$

$\frac{5 y - 3}{2} = 6$

$x = y - 3$

$\frac{5 y - 3}{2} = 6$

$x = y - 3$

$\frac{5 y - 3}{2} = 6$

$x = y - 3$

Solve for $y$ in $\frac{5 y - 3}{2} = 6$ .

Multiply both sides by $2$ .

$\frac{5 y - 3}{2} \cdot 2 = 6 \cdot 2$

$x = y - 3$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 y - 3}{2} \cdot 2 = 6 \cdot 2$

$x = y - 3$

Rewrite the expression.

$5 y - 3 = 6 \cdot 2$

$x = y - 3$

$5 y - 3 = 6 \cdot 2$

$x = y - 3$

$5 y - 3 = 6 \cdot 2$

$x = y - 3$

Simplify the right side.

Multiply $6$ by $2$ .

$5 y - 3 = 12$

$x = y - 3$

$5 y - 3 = 12$

$x = y - 3$

$5 y - 3 = 12$

$x = y - 3$

Solve for $y$ .

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

Add $3$ to both sides of the equation.

$5 y = 12 + 3$

$x = y - 3$

Add $12$ and $3$ .

$5 y = 15$

$x = y - 3$

$5 y = 15$

$x = y - 3$

Divide each term in $5 y = 15$ by $5$ and simplify.

Divide each term in $5 y = 15$ by $5$ .

$\frac{5 y}{5} = \frac{15}{5}$

$x = y - 3$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{15}{5}$

$x = y - 3$

Divide $y$ by $1$ .

$y = \frac{15}{5}$

$x = y - 3$

$y = \frac{15}{5}$

$x = y - 3$

$y = \frac{15}{5}$

$x = y - 3$

Simplify the right side.

Divide $15$ by $5$ .

$y = 3$

$x = y - 3$

$y = 3$

$x = y - 3$

$y = 3$

$x = y - 3$

$y = 3$

$x = y - 3$

$y = 3$

$x = y - 3$

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

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

$x = (3) - 3$

$y = 3$

Simplify the right side.

Subtract $3$ from $3$ .

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

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

$(0, 3)$

The result can be shown in multiple forms.

Point Form:

$(0, 3)$

Equation Form:

$x = 0, y = 3$

Solve the System of Equations x=y-3 x/2+2y=6

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