Solve the System of Equations x+y=27 y=x+3

$x + y = 27$ $y = x + 3$

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

Replace all occurrences of $y$ in $x + y = 27$ with $x + 3$ .

$x + x + 3 = 27$

$y = x + 3$

Simplify the left side.

Simplify $x + x + 3$ .

Remove parentheses.

$x + x + 3 = 27$

$y = x + 3$

Add $x$ and $x$ .

$2 x + 3 = 27$

$y = x + 3$

$2 x + 3 = 27$

$y = x + 3$

$2 x + 3 = 27$

$y = x + 3$

$2 x + 3 = 27$

$y = x + 3$

Solve for $x$ in $2 x + 3 = 27$ .

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

Subtract $3$ from both sides of the equation.

$2 x = 27 - 3$

$y = x + 3$

Subtract $3$ from $27$ .

$2 x = 24$

$y = x + 3$

$2 x = 24$

$y = x + 3$

Divide each term in $2 x = 24$ by $2$ and simplify.

Divide each term in $2 x = 24$ by $2$ .

$\frac{2 x}{2} = \frac{24}{2}$

$y = x + 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{24}{2}$

$y = x + 3$

Divide $x$ by $1$ .

$x = \frac{24}{2}$

$y = x + 3$

$x = \frac{24}{2}$

$y = x + 3$

$x = \frac{24}{2}$

$y = x + 3$

Simplify the right side.

Divide $24$ by $2$ .

$x = 12$

$y = x + 3$

$x = 12$

$y = x + 3$

$x = 12$

$y = x + 3$

$x = 12$

$y = x + 3$

Replace all occurrences of $x$ with $12$ in each equation.

Replace all occurrences of $x$ in $y = x + 3$ with $12$ .

$y = (12) + 3$

$x = 12$

Simplify the right side.

Add $12$ and $3$ .

$y = 15$

$x = 12$

$y = 15$

$x = 12$

$y = 15$

$x = 12$

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

$(12, 15)$

The result can be shown in multiple forms.

Point Form:

$(12, 15)$

Equation Form:

$x = 12, y = 15$

Solve the System of Equations x+y=27 y=x+3

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