Solve the System of Equations 5x-4y=-10 y=2x-5

$5 x - 4 y = - 10$ $y = 2 x - 5$

Replace all occurrences of $y$ with $2 x - 5$ in each equation.

Replace all occurrences of $y$ in $5 x - 4 y = - 10$ with $2 x - 5$ .

$5 x - 4 (2 x - 5) = - 10$

$y = 2 x - 5$

Simplify the left side.

Simplify $5 x - 4 (2 x - 5)$ .

Simplify each term.

Apply the distributive property.

$5 x - 4 (2 x) - 4 \cdot - 5 = - 10$

$y = 2 x - 5$

Multiply $2$ by $- 4$ .

$5 x - 8 x - 4 \cdot - 5 = - 10$

$y = 2 x - 5$

Multiply $- 4$ by $- 5$ .

$5 x - 8 x + 20 = - 10$

$y = 2 x - 5$

$5 x - 8 x + 20 = - 10$

$y = 2 x - 5$

Subtract $8 x$ from $5 x$ .

$- 3 x + 20 = - 10$

$y = 2 x - 5$

$- 3 x + 20 = - 10$

$y = 2 x - 5$

$- 3 x + 20 = - 10$

$y = 2 x - 5$

$- 3 x + 20 = - 10$

$y = 2 x - 5$

Solve for $x$ in $- 3 x + 20 = - 10$ .

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

Subtract $20$ from both sides of the equation.

$- 3 x = - 10 - 20$

$y = 2 x - 5$

Subtract $20$ from $- 10$ .

$- 3 x = - 30$

$y = 2 x - 5$

$- 3 x = - 30$

$y = 2 x - 5$

Divide each term in $- 3 x = - 30$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 30$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 30}{- 3}$

$y = 2 x - 5$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 30}{- 3}$

$y = 2 x - 5$

Divide $x$ by $1$ .

$x = \frac{- 30}{- 3}$

$y = 2 x - 5$

$x = \frac{- 30}{- 3}$

$y = 2 x - 5$

$x = \frac{- 30}{- 3}$

$y = 2 x - 5$

Simplify the right side.

Divide $- 30$ by $- 3$ .

$x = 10$

$y = 2 x - 5$

$x = 10$

$y = 2 x - 5$

$x = 10$

$y = 2 x - 5$

$x = 10$

$y = 2 x - 5$

Replace all occurrences of $x$ with $10$ in each equation.

Replace all occurrences of $x$ in $y = 2 x - 5$ with $10$ .

$y = 2 (10) - 5$

$x = 10$

Simplify the right side.

Simplify $2 (10) - 5$ .

Multiply $2$ by $10$ .

$y = 20 - 5$

$x = 10$

Subtract $5$ from $20$ .

$y = 15$

$x = 10$

$y = 15$

$x = 10$

$y = 15$

$x = 10$

$y = 15$

$x = 10$

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

$(10, 15)$

The result can be shown in multiple forms.

Point Form:

$(10, 15)$

Equation Form:

$x = 10, y = 15$

Solve the System of Equations 5x-4y=-10 y=2x-5

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