Solve by Substitution y=-2x+6 3y-x+3=0

$y = - 2 x + 6$ $3 y - x + 3 = 0$

Step 1

Replace all occurrences of $y$ with $- 2 x + 6$ in each equation.

Replace all occurrences of $y$ in $3 y - x + 3 = 0$ with $- 2 x + 6$ .

$3 (- 2 x + 6) - x + 3 = 0$

$y = - 2 x + 6$

Simplify the left side.

Simplify $3 (- 2 x + 6) - x + 3$ .

Simplify each term.

Apply the distributive property.

$3 (- 2 x) + 3 \cdot 6 - x + 3 = 0$

$y = - 2 x + 6$

Multiply $- 2$ by $3$ .

$- 6 x + 3 \cdot 6 - x + 3 = 0$

$y = - 2 x + 6$

Multiply $3$ by $6$ .

$- 6 x + 18 - x + 3 = 0$

$y = - 2 x + 6$

$- 6 x + 18 - x + 3 = 0$

$y = - 2 x + 6$

Simplify by adding terms.

Subtract $x$ from $- 6 x$ .

$- 7 x + 18 + 3 = 0$

$y = - 2 x + 6$

Add $18$ and $3$ .

$- 7 x + 21 = 0$

$y = - 2 x + 6$

$- 7 x + 21 = 0$

$y = - 2 x + 6$

$- 7 x + 21 = 0$

$y = - 2 x + 6$

$- 7 x + 21 = 0$

$y = - 2 x + 6$

$- 7 x + 21 = 0$

$y = - 2 x + 6$

Step 2

Solve for $x$ in $- 7 x + 21 = 0$ .

Subtract $21$ from both sides of the equation.

$- 7 x = - 21$

$y = - 2 x + 6$

Divide each term in $- 7 x = - 21$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 21$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 21}{- 7}$

$y = - 2 x + 6$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 21}{- 7}$

$y = - 2 x + 6$

Divide $x$ by $1$ .

$x = \frac{- 21}{- 7}$

$y = - 2 x + 6$

$x = \frac{- 21}{- 7}$

$y = - 2 x + 6$

$x = \frac{- 21}{- 7}$

$y = - 2 x + 6$

Simplify the right side.

Divide $- 21$ by $- 7$ .

$x = 3$

$y = - 2 x + 6$

$x = 3$

$y = - 2 x + 6$

$x = 3$

$y = - 2 x + 6$

$x = 3$

$y = - 2 x + 6$

Step 3

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

Replace all occurrences of $x$ in $y = - 2 x + 6$ with $3$ .

$y = - 2 \cdot 3 + 6$

$x = 3$

Simplify the right side.

Simplify $- 2 \cdot 3 + 6$ .

Multiply $- 2$ by $3$ .

$y = - 6 + 6$

$x = 3$

Add $- 6$ and $6$ .

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

Step 4

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

$(3, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 0)$

Equation Form:

$x = 3, y = 0$

Step 6

Solve by Substitution y=-2x+6 3y-x+3=0

Related Questions

Support LCMGCF.com by disabling your adblocker.