Solve by Substitution 5x+y=19 2y=-5x+28

$5 x + y = 19$ $2 y = - 5 x + 28$

Step 1

Subtract $5 x$ from both sides of the equation.

$y = 19 - 5 x$

$2 y = - 5 x + 28$

Step 2

Replace all occurrences of $y$ with $19 - 5 x$ in each equation.

Replace all occurrences of $y$ in $2 y = - 5 x + 28$ with $19 - 5 x$ .

$2 (19 - 5 x) = - 5 x + 28$

$y = 19 - 5 x$

Simplify the left side.

Simplify $2 (19 - 5 x)$ .

Apply the distributive property.

$2 \cdot 19 + 2 (- 5 x) = - 5 x + 28$

$y = 19 - 5 x$

Multiply.

Multiply $2$ by $19$ .

$38 + 2 (- 5 x) = - 5 x + 28$

$y = 19 - 5 x$

Multiply $- 5$ by $2$ .

$38 - 10 x = - 5 x + 28$

$y = 19 - 5 x$

$38 - 10 x = - 5 x + 28$

$y = 19 - 5 x$

$38 - 10 x = - 5 x + 28$

$y = 19 - 5 x$

$38 - 10 x = - 5 x + 28$

$y = 19 - 5 x$

$38 - 10 x = - 5 x + 28$

$y = 19 - 5 x$

Step 3

Solve for $x$ in $38 - 10 x = - 5 x + 28$ .

Move all terms containing $x$ to the left side of the equation.

Add $5 x$ to both sides of the equation.

$38 - 10 x + 5 x = 28$

$y = 19 - 5 x$

Add $- 10 x$ and $5 x$ .

$38 - 5 x = 28$

$y = 19 - 5 x$

$38 - 5 x = 28$

$y = 19 - 5 x$

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

Subtract $38$ from both sides of the equation.

$- 5 x = 28 - 38$

$y = 19 - 5 x$

Subtract $38$ from $28$ .

$- 5 x = - 10$

$y = 19 - 5 x$

$- 5 x = - 10$

$y = 19 - 5 x$

Divide each term in $- 5 x = - 10$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

$y = 19 - 5 x$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

$y = 19 - 5 x$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 5}$

$y = 19 - 5 x$

$x = \frac{- 10}{- 5}$

$y = 19 - 5 x$

$x = \frac{- 10}{- 5}$

$y = 19 - 5 x$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$x = 2$

$y = 19 - 5 x$

$x = 2$

$y = 19 - 5 x$

$x = 2$

$y = 19 - 5 x$

$x = 2$

$y = 19 - 5 x$

Step 4

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

Replace all occurrences of $x$ in $y = 19 - 5 x$ with $2$ .

$y = 19 - 5 \cdot 2$

$x = 2$

Simplify the right side.

Simplify $19 - 5 \cdot 2$ .

Multiply $- 5$ by $2$ .

$y = 19 - 10$

$x = 2$

Subtract $10$ from $19$ .

$y = 9$

$x = 2$

$y = 9$

$x = 2$

$y = 9$

$x = 2$

$y = 9$

$x = 2$

Step 5

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

$(2, 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 9)$

Equation Form:

$x = 2, y = 9$

Step 7

Solve by Substitution 5x+y=19 2y=-5x+28

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