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

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

Add $2 x$ to both sides of the equation.

$y = - 6 + 2 x$

$4 x + 3 y = 2$

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

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

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

$y = - 6 + 2 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = - 6 + 2 x$

Multiply $3$ by $- 6$ .

$4 x - 18 + 3 (2 x) = 2$

$y = - 6 + 2 x$

Multiply $2$ by $3$ .

$4 x - 18 + 6 x = 2$

$y = - 6 + 2 x$

$4 x - 18 + 6 x = 2$

$y = - 6 + 2 x$

Add $4 x$ and $6 x$ .

$10 x - 18 = 2$

$y = - 6 + 2 x$

$10 x - 18 = 2$

$y = - 6 + 2 x$

$10 x - 18 = 2$

$y = - 6 + 2 x$

$10 x - 18 = 2$

$y = - 6 + 2 x$

Solve for $x$ in $10 x - 18 = 2$ .

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

Add $18$ to both sides of the equation.

$10 x = 2 + 18$

$y = - 6 + 2 x$

Add $2$ and $18$ .

$10 x = 20$

$y = - 6 + 2 x$

$10 x = 20$

$y = - 6 + 2 x$

Divide each term in $10 x = 20$ by $10$ and simplify.

Divide each term in $10 x = 20$ by $10$ .

$\frac{10 x}{10} = \frac{20}{10}$

$y = - 6 + 2 x$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{20}{10}$

$y = - 6 + 2 x$

Divide $x$ by $1$ .

$x = \frac{20}{10}$

$y = - 6 + 2 x$

$x = \frac{20}{10}$

$y = - 6 + 2 x$

$x = \frac{20}{10}$

$y = - 6 + 2 x$

Simplify the right side.

Divide $20$ by $10$ .

$x = 2$

$y = - 6 + 2 x$

$x = 2$

$y = - 6 + 2 x$

$x = 2$

$y = - 6 + 2 x$

$x = 2$

$y = - 6 + 2 x$

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

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

$y = - 6 + 2 (2)$

$x = 2$

Simplify the right side.

Simplify $- 6 + 2 (2)$ .

Multiply $2$ by $2$ .

$y = - 6 + 4$

$x = 2$

Add $- 6$ and $4$ .

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

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

$(2, - 2)$

The result can be shown in multiple forms.

Point Form:

$(2, - 2)$

Equation Form:

$x = 2, y = - 2$

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

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