Solve by Substitution 2x+9y=27 and x-3y=-24

$2 x + 9 y = 27$ and $x - 3 y = - 24$

Add $3 y$ to both sides of the equation.

$x = - 24 + 3 y$

$2 x + 9 y = 27$

Replace all occurrences of $x$ with $- 24 + 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x + 9 y = 27$ with $- 24 + 3 y$ .

$2 (- 24 + 3 y) + 9 y = 27$

$x = - 24 + 3 y$

Simplify the left side.

Simplify $2 (- 24 + 3 y) + 9 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 24 + 2 (3 y) + 9 y = 27$

$x = - 24 + 3 y$

Multiply $2$ by $- 24$ .

$- 48 + 2 (3 y) + 9 y = 27$

$x = - 24 + 3 y$

Multiply $3$ by $2$ .

$- 48 + 6 y + 9 y = 27$

$x = - 24 + 3 y$

$- 48 + 6 y + 9 y = 27$

$x = - 24 + 3 y$

Add $6 y$ and $9 y$ .

$- 48 + 15 y = 27$

$x = - 24 + 3 y$

$- 48 + 15 y = 27$

$x = - 24 + 3 y$

$- 48 + 15 y = 27$

$x = - 24 + 3 y$

$- 48 + 15 y = 27$

$x = - 24 + 3 y$

Solve for $y$ in $- 48 + 15 y = 27$ .

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

Add $48$ to both sides of the equation.

$15 y = 27 + 48$

$x = - 24 + 3 y$

Add $27$ and $48$ .

$15 y = 75$

$x = - 24 + 3 y$

$15 y = 75$

$x = - 24 + 3 y$

Divide each term in $15 y = 75$ by $15$ and simplify.

Divide each term in $15 y = 75$ by $15$ .

$\frac{15 y}{15} = \frac{75}{15}$

$x = - 24 + 3 y$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{75}{15}$

$x = - 24 + 3 y$

Divide $y$ by $1$ .

$y = \frac{75}{15}$

$x = - 24 + 3 y$

$y = \frac{75}{15}$

$x = - 24 + 3 y$

$y = \frac{75}{15}$

$x = - 24 + 3 y$

Simplify the right side.

Divide $75$ by $15$ .

$y = 5$

$x = - 24 + 3 y$

$y = 5$

$x = - 24 + 3 y$

$y = 5$

$x = - 24 + 3 y$

$y = 5$

$x = - 24 + 3 y$

Replace all occurrences of $y$ with $5$ in each equation.

Replace all occurrences of $y$ in $x = - 24 + 3 y$ with $5$ .

$x = - 24 + 3 (5)$

$y = 5$

Simplify the right side.

Simplify $- 24 + 3 (5)$ .

Multiply $3$ by $5$ .

$x = - 24 + 15$

$y = 5$

Add $- 24$ and $15$ .

$x = - 9$

$y = 5$

$x = - 9$

$y = 5$

$x = - 9$

$y = 5$

$x = - 9$

$y = 5$

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

$(- 9, 5)$

The result can be shown in multiple forms.

Point Form:

$(- 9, 5)$

Equation Form:

$x = - 9, y = 5$

Solve by Substitution 2x+9y=27 and x-3y=-24

Related Questions

Support LCMGCF.com by disabling your adblocker.