Solve the System of Equations x+3y=7 2x-4y=24

$x + 3 y = 7$ $2 x - 4 y = 24$

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

$x = 7 - 3 y$

$2 x - 4 y = 24$

Replace all occurrences of $x$ with $7 - 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x - 4 y = 24$ with $7 - 3 y$ .

$2 (7 - 3 y) - 4 y = 24$

$x = 7 - 3 y$

Simplify the left side.

Simplify $2 (7 - 3 y) - 4 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 7 + 2 (- 3 y) - 4 y = 24$

$x = 7 - 3 y$

Multiply $2$ by $7$ .

$14 + 2 (- 3 y) - 4 y = 24$

$x = 7 - 3 y$

Multiply $- 3$ by $2$ .

$14 - 6 y - 4 y = 24$

$x = 7 - 3 y$

$14 - 6 y - 4 y = 24$

$x = 7 - 3 y$

Subtract $4 y$ from $- 6 y$ .

$14 - 10 y = 24$

$x = 7 - 3 y$

$14 - 10 y = 24$

$x = 7 - 3 y$

$14 - 10 y = 24$

$x = 7 - 3 y$

$14 - 10 y = 24$

$x = 7 - 3 y$

Solve for $y$ in $14 - 10 y = 24$ .

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

Subtract $14$ from both sides of the equation.

$- 10 y = 24 - 14$

$x = 7 - 3 y$

Subtract $14$ from $24$ .

$- 10 y = 10$

$x = 7 - 3 y$

$- 10 y = 10$

$x = 7 - 3 y$

Divide each term in $- 10 y = 10$ by $- 10$ and simplify.

Divide each term in $- 10 y = 10$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{10}{- 10}$

$x = 7 - 3 y$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{10}{- 10}$

$x = 7 - 3 y$

Divide $y$ by $1$ .

$y = \frac{10}{- 10}$

$x = 7 - 3 y$

$y = \frac{10}{- 10}$

$x = 7 - 3 y$

$y = \frac{10}{- 10}$

$x = 7 - 3 y$

Simplify the right side.

Divide $10$ by $- 10$ .

$y = - 1$

$x = 7 - 3 y$

$y = - 1$

$x = 7 - 3 y$

$y = - 1$

$x = 7 - 3 y$

$y = - 1$

$x = 7 - 3 y$

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = 7 - 3 y$ with $- 1$ .

$x = 7 - 3 \cdot - 1$

$y = - 1$

Simplify the right side.

Simplify $7 - 3 \cdot - 1$ .

Multiply $- 3$ by $- 1$ .

$x = 7 + 3$

$y = - 1$

Add $7$ and $3$ .

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

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

$(10, - 1)$

The result can be shown in multiple forms.

Point Form:

$(10, - 1)$

Equation Form:

$x = 10, y = - 1$

Solve the System of Equations x+3y=7 2x-4y=24

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