Solve by Substitution -5x+y=-3 and 3x-8y=24

$- 5 x + y = - 3$ and $3 x - 8 y = 24$

Step 1

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

$y = - 3 + 5 x$

$3 x - 8 y = 24$

Step 2

Replace all occurrences of $y$ with $- 3 + 5 x$ in each equation.

Replace all occurrences of $y$ in $3 x - 8 y = 24$ with $- 3 + 5 x$ .

$3 x - 8 (- 3 + 5 x) = 24$

$y = - 3 + 5 x$

Simplify the left side.

Simplify $3 x - 8 (- 3 + 5 x)$ .

Simplify each term.

Apply the distributive property.

$3 x - 8 \cdot - 3 - 8 (5 x) = 24$

$y = - 3 + 5 x$

Multiply $- 8$ by $- 3$ .

$3 x + 24 - 8 (5 x) = 24$

$y = - 3 + 5 x$

Multiply $5$ by $- 8$ .

$3 x + 24 - 40 x = 24$

$y = - 3 + 5 x$

$3 x + 24 - 40 x = 24$

$y = - 3 + 5 x$

Subtract $40 x$ from $3 x$ .

$- 37 x + 24 = 24$

$y = - 3 + 5 x$

$- 37 x + 24 = 24$

$y = - 3 + 5 x$

$- 37 x + 24 = 24$

$y = - 3 + 5 x$

$- 37 x + 24 = 24$

$y = - 3 + 5 x$

Step 3

Solve for $x$ in $- 37 x + 24 = 24$ .

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

Subtract $24$ from both sides of the equation.

$- 37 x = 24 - 24$

$y = - 3 + 5 x$

Subtract $24$ from $24$ .

$- 37 x = 0$

$y = - 3 + 5 x$

$- 37 x = 0$

$y = - 3 + 5 x$

Divide each term in $- 37 x = 0$ by $- 37$ and simplify.

Divide each term in $- 37 x = 0$ by $- 37$ .

$\frac{- 37 x}{- 37} = \frac{0}{- 37}$

$y = - 3 + 5 x$

Simplify the left side.

Cancel the common factor of $- 37$ .

Cancel the common factor.

$\frac{- 37 x}{- 37} = \frac{0}{- 37}$

$y = - 3 + 5 x$

Divide $x$ by $1$ .

$x = \frac{0}{- 37}$

$y = - 3 + 5 x$

$x = \frac{0}{- 37}$

$y = - 3 + 5 x$

$x = \frac{0}{- 37}$

$y = - 3 + 5 x$

Simplify the right side.

Divide $0$ by $- 37$ .

$x = 0$

$y = - 3 + 5 x$

$x = 0$

$y = - 3 + 5 x$

$x = 0$

$y = - 3 + 5 x$

$x = 0$

$y = - 3 + 5 x$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = - 3 + 5 x$ with $0$ .

$y = - 3 + 5 (0)$

$x = 0$

Simplify the right side.

Simplify $- 3 + 5 (0)$ .

Multiply $5$ by $0$ .

$y = - 3 + 0$

$x = 0$

Add $- 3$ and $0$ .

$y = - 3$

$x = 0$

$y = - 3$

$x = 0$

$y = - 3$

$x = 0$

$y = - 3$

$x = 0$

Step 5

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

$(0, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 3)$

Equation Form:

$x = 0, y = - 3$

Step 7

Solve by Substitution -5x+y=-3 and 3x-8y=24

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