Solve by Substitution y=-3x+5 and 5x-4y=-3

$y = - 3 x + 5$ and $5 x - 4 y = - 3$

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

Replace all occurrences of $y$ in $5 x - 4 y = - 3$ with $- 3 x + 5$ .

$5 x - 4 (- 3 x + 5) = - 3$

$y = - 3 x + 5$

Simplify the left side.

Simplify $5 x - 4 (- 3 x + 5)$ .

Simplify each term.

Apply the distributive property.

$5 x - 4 (- 3 x) - 4 \cdot 5 = - 3$

$y = - 3 x + 5$

Multiply $- 3$ by $- 4$ .

$5 x + 12 x - 4 \cdot 5 = - 3$

$y = - 3 x + 5$

Multiply $- 4$ by $5$ .

$5 x + 12 x - 20 = - 3$

$y = - 3 x + 5$

$5 x + 12 x - 20 = - 3$

$y = - 3 x + 5$

Add $5 x$ and $12 x$ .

$17 x - 20 = - 3$

$y = - 3 x + 5$

$17 x - 20 = - 3$

$y = - 3 x + 5$

$17 x - 20 = - 3$

$y = - 3 x + 5$

$17 x - 20 = - 3$

$y = - 3 x + 5$

Solve for $x$ in $17 x - 20 = - 3$ .

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

Add $20$ to both sides of the equation.

$17 x = - 3 + 20$

$y = - 3 x + 5$

Add $- 3$ and $20$ .

$17 x = 17$

$y = - 3 x + 5$

$17 x = 17$

$y = - 3 x + 5$

Divide each term in $17 x = 17$ by $17$ and simplify.

Divide each term in $17 x = 17$ by $17$ .

$\frac{17 x}{17} = \frac{17}{17}$

$y = - 3 x + 5$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} = \frac{17}{17}$

$y = - 3 x + 5$

Divide $x$ by $1$ .

$x = \frac{17}{17}$

$y = - 3 x + 5$

$x = \frac{17}{17}$

$y = - 3 x + 5$

$x = \frac{17}{17}$

$y = - 3 x + 5$

Simplify the right side.

Divide $17$ by $17$ .

$x = 1$

$y = - 3 x + 5$

$x = 1$

$y = - 3 x + 5$

$x = 1$

$y = - 3 x + 5$

$x = 1$

$y = - 3 x + 5$

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = - 3 x + 5$ with $1$ .

$y = - 3 \cdot 1 + 5$

$x = 1$

Simplify the right side.

Simplify $- 3 \cdot 1 + 5$ .

Multiply $- 3$ by $1$ .

$y = - 3 + 5$

$x = 1$

Add $- 3$ and $5$ .

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

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

$(1, 2)$

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Solve by Substitution y=-3x+5 and 5x-4y=-3

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