Solve by Substitution -5x+3y=51 and y=10x-8

$- 5 x + 3 y = 51$ and $y = 10 x - 8$

Replace all occurrences of $y$ with $10 x - 8$ in each equation.

Replace all occurrences of $y$ in $- 5 x + 3 y = 51$ with $10 x - 8$ .

$- 5 x + 3 (10 x - 8) = 51$

$y = 10 x - 8$

Simplify the left side.

Simplify $- 5 x + 3 (10 x - 8)$ .

Simplify each term.

Apply the distributive property.

$- 5 x + 3 (10 x) + 3 \cdot - 8 = 51$

$y = 10 x - 8$

Multiply $10$ by $3$ .

$- 5 x + 30 x + 3 \cdot - 8 = 51$

$y = 10 x - 8$

Multiply $3$ by $- 8$ .

$- 5 x + 30 x - 24 = 51$

$y = 10 x - 8$

$- 5 x + 30 x - 24 = 51$

$y = 10 x - 8$

Add $- 5 x$ and $30 x$ .

$25 x - 24 = 51$

$y = 10 x - 8$

$25 x - 24 = 51$

$y = 10 x - 8$

$25 x - 24 = 51$

$y = 10 x - 8$

$25 x - 24 = 51$

$y = 10 x - 8$

Solve for $x$ in $25 x - 24 = 51$ .

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

Add $24$ to both sides of the equation.

$25 x = 51 + 24$

$y = 10 x - 8$

Add $51$ and $24$ .

$25 x = 75$

$y = 10 x - 8$

$25 x = 75$

$y = 10 x - 8$

Divide each term in $25 x = 75$ by $25$ and simplify.

Divide each term in $25 x = 75$ by $25$ .

$\frac{25 x}{25} = \frac{75}{25}$

$y = 10 x - 8$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x}{25} = \frac{75}{25}$

$y = 10 x - 8$

Divide $x$ by $1$ .

$x = \frac{75}{25}$

$y = 10 x - 8$

$x = \frac{75}{25}$

$y = 10 x - 8$

$x = \frac{75}{25}$

$y = 10 x - 8$

Simplify the right side.

Divide $75$ by $25$ .

$x = 3$

$y = 10 x - 8$

$x = 3$

$y = 10 x - 8$

$x = 3$

$y = 10 x - 8$

$x = 3$

$y = 10 x - 8$

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

Replace all occurrences of $x$ in $y = 10 x - 8$ with $3$ .

$y = 10 (3) - 8$

$x = 3$

Simplify the right side.

Simplify $10 (3) - 8$ .

Multiply $10$ by $3$ .

$y = 30 - 8$

$x = 3$

Subtract $8$ from $30$ .

$y = 22$

$x = 3$

$y = 22$

$x = 3$

$y = 22$

$x = 3$

$y = 22$

$x = 3$

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

$(3, 22)$

The result can be shown in multiple forms.

Point Form:

$(3, 22)$

Equation Form:

$x = 3, y = 22$

Solve by Substitution -5x+3y=51 and y=10x-8

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