Solve the System of Equations y=-5x+3 y=1

$y = - 5 x + 3$ $y = 1$

Step 1

Eliminate the equal sides of each equation and combine.

$- 5 x + 3 = 1$

Step 2

Solve $- 5 x + 3 = 1$ for $x$ .

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

Subtract $3$ from both sides of the equation.

$- 5 x = 1 - 3$

Subtract $3$ from $1$ .

$- 5 x = - 2$

Divide each term in $- 5 x = - 2$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 2$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 2}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 2}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{2}{5}$

Step 3

Substitute $\frac{2}{5}$ for $x$ .

$y = 1$

Step 4

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

$(\frac{2}{5}, 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{2}{5}, 1)$

Equation Form:

$x = \frac{2}{5}, y = 1$

Step 6