Solve the System of Equations 5x=y+6 5x+2y=3

$5 x = y + 6$ $5 x + 2 y = 3$

Step 1

Divide each term in $5 x = y + 6$ by $5$ and simplify.

Divide each term in $5 x = y + 6$ by $5$ .

$\frac{5 x}{5} = \frac{y}{5} + \frac{6}{5}$

$5 x + 2 y = 3$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{y}{5} + \frac{6}{5}$

$5 x + 2 y = 3$

Divide $x$ by $1$ .

$x = \frac{y}{5} + \frac{6}{5}$

$5 x + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$5 x + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$5 x + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$5 x + 2 y = 3$

Step 2

Replace all occurrences of $x$ with $\frac{y}{5} + \frac{6}{5}$ in each equation.

Replace all occurrences of $x$ in $5 x + 2 y = 3$ with $\frac{y}{5} + \frac{6}{5}$ .

$5 (\frac{y}{5} + \frac{6}{5}) + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Simplify the left side.

Simplify $5 (\frac{y}{5} + \frac{6}{5}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$5 (\frac{y}{5}) + 5 (\frac{6}{5}) + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$5 (\frac{y}{5}) + 5 (\frac{6}{5}) + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Rewrite the expression.

$y + 5 (\frac{6}{5}) + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$y + 5 (\frac{6}{5}) + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$y + 5 (\frac{6}{5}) + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Rewrite the expression.

$y + 6 + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$y + 6 + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$y + 6 + 2 y = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Add $y$ and $2 y$ .

$3 y + 6 = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$3 y + 6 = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$3 y + 6 = 3$

$x = \frac{y}{5} + \frac{6}{5}$

$3 y + 6 = 3$

$x = \frac{y}{5} + \frac{6}{5}$

Step 3

Solve for $y$ in $3 y + 6 = 3$ .

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

Subtract $6$ from both sides of the equation.

$3 y = 3 - 6$

$x = \frac{y}{5} + \frac{6}{5}$

Subtract $6$ from $3$ .

$3 y = - 3$

$x = \frac{y}{5} + \frac{6}{5}$

$3 y = - 3$

$x = \frac{y}{5} + \frac{6}{5}$

Divide each term in $3 y = - 3$ by $3$ and simplify.

Divide each term in $3 y = - 3$ by $3$ .

$\frac{3 y}{3} = \frac{- 3}{3}$

$x = \frac{y}{5} + \frac{6}{5}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 3}{3}$

$x = \frac{y}{5} + \frac{6}{5}$

Divide $y$ by $1$ .

$y = \frac{- 3}{3}$

$x = \frac{y}{5} + \frac{6}{5}$

$y = \frac{- 3}{3}$

$x = \frac{y}{5} + \frac{6}{5}$

$y = \frac{- 3}{3}$

$x = \frac{y}{5} + \frac{6}{5}$

Simplify the right side.

Divide $- 3$ by $3$ .

$y = - 1$

$x = \frac{y}{5} + \frac{6}{5}$

$y = - 1$

$x = \frac{y}{5} + \frac{6}{5}$

$y = - 1$

$x = \frac{y}{5} + \frac{6}{5}$

$y = - 1$

$x = \frac{y}{5} + \frac{6}{5}$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{y}{5} + \frac{6}{5}$ with $- 1$ .

$x = \frac{- 1}{5} + \frac{6}{5}$

$y = - 1$

Simplify the right side.

Simplify $\frac{- 1}{5} + \frac{6}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{- 1 + 6}{5}$

$y = - 1$

Simplify the expression.

Add $- 1$ and $6$ .

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

$y = - 1$

Divide $5$ by $5$ .

$x = 1$

$y = - 1$

$x = 1$

$y = - 1$

$x = 1$

$y = - 1$

$x = 1$

$y = - 1$

$x = 1$

$y = - 1$

Step 5

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

$(1, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 1)$

Equation Form:

$x = 1, y = - 1$

Step 7

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