Solve the System of Equations Y=-3x+4 x=2Y+6

$Y = - 3 x + 4$ $x = 2 Y + 6$

Step 1

Replace all occurrences of $Y$ with $- 3 x + 4$ in each equation.

Replace all occurrences of $Y$ in $x = 2 Y + 6$ with $- 3 x + 4$ .

$x = 2 (- 3 x + 4) + 6$

$Y = - 3 x + 4$

Simplify the right side.

Simplify $2 (- 3 x + 4) + 6$ .

Simplify each term.

Apply the distributive property.

$x = 2 (- 3 x) + 2 \cdot 4 + 6$

$Y = - 3 x + 4$

Multiply $- 3$ by $2$ .

$x = - 6 x + 2 \cdot 4 + 6$

$Y = - 3 x + 4$

Multiply $2$ by $4$ .

$x = - 6 x + 8 + 6$

$Y = - 3 x + 4$

$x = - 6 x + 8 + 6$

$Y = - 3 x + 4$

Add $8$ and $6$ .

$x = - 6 x + 14$

$Y = - 3 x + 4$

$x = - 6 x + 14$

$Y = - 3 x + 4$

$x = - 6 x + 14$

$Y = - 3 x + 4$

$x = - 6 x + 14$

$Y = - 3 x + 4$

Step 2

Solve for $x$ in $x = - 6 x + 14$ .

Move all terms containing $x$ to the left side of the equation.

Add $6 x$ to both sides of the equation.

$x + 6 x = 14$

$Y = - 3 x + 4$

Add $x$ and $6 x$ .

$7 x = 14$

$Y = - 3 x + 4$

$7 x = 14$

$Y = - 3 x + 4$

Divide each term in $7 x = 14$ by $7$ and simplify.

Divide each term in $7 x = 14$ by $7$ .

$\frac{7 x}{7} = \frac{14}{7}$

$Y = - 3 x + 4$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{14}{7}$

$Y = - 3 x + 4$

Divide $x$ by $1$ .

$x = \frac{14}{7}$

$Y = - 3 x + 4$

$x = \frac{14}{7}$

$Y = - 3 x + 4$

$x = \frac{14}{7}$

$Y = - 3 x + 4$

Simplify the right side.

Divide $14$ by $7$ .

$x = 2$

$Y = - 3 x + 4$

$x = 2$

$Y = - 3 x + 4$

$x = 2$

$Y = - 3 x + 4$

$x = 2$

$Y = - 3 x + 4$

Step 3

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $Y = - 3 x + 4$ with $2$ .

$Y = - 3 \cdot 2 + 4$

$x = 2$

Simplify the right side.

Simplify $- 3 \cdot 2 + 4$ .

Multiply $- 3$ by $2$ .

$Y = - 6 + 4$

$x = 2$

Add $- 6$ and $4$ .

$Y = - 2$

$x = 2$

$Y = - 2$

$x = 2$

$Y = - 2$

$x = 2$

$Y = - 2$

$x = 2$

Step 4

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

$(2, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, - 2)$

Equation Form:

$x = 2, y = - 2$

Step 6

Solve the System of Equations Y=-3x+4 x=2Y+6

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