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

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

Step 1

Subtract $4 x$ from both sides of the equation.

$y = 6 - 4 x$

$2 x - 3 y = - 4$

Step 2

Replace all occurrences of $y$ with $6 - 4 x$ in each equation.

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

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

$y = 6 - 4 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = 6 - 4 x$

Multiply $- 3$ by $6$ .

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

$y = 6 - 4 x$

Multiply $- 4$ by $- 3$ .

$2 x - 18 + 12 x = - 4$

$y = 6 - 4 x$

$2 x - 18 + 12 x = - 4$

$y = 6 - 4 x$

Add $2 x$ and $12 x$ .

$14 x - 18 = - 4$

$y = 6 - 4 x$

$14 x - 18 = - 4$

$y = 6 - 4 x$

$14 x - 18 = - 4$

$y = 6 - 4 x$

$14 x - 18 = - 4$

$y = 6 - 4 x$

Step 3

Solve for $x$ in $14 x - 18 = - 4$ .

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

Add $18$ to both sides of the equation.

$14 x = - 4 + 18$

$y = 6 - 4 x$

Add $- 4$ and $18$ .

$14 x = 14$

$y = 6 - 4 x$

$14 x = 14$

$y = 6 - 4 x$

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

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

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

$y = 6 - 4 x$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

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

$y = 6 - 4 x$

Divide $x$ by $1$ .

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

$y = 6 - 4 x$

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

$y = 6 - 4 x$

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

$y = 6 - 4 x$

Simplify the right side.

Divide $14$ by $14$ .

$x = 1$

$y = 6 - 4 x$

$x = 1$

$y = 6 - 4 x$

$x = 1$

$y = 6 - 4 x$

$x = 1$

$y = 6 - 4 x$

Step 4

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = 6 - 4 x$ with $1$ .

$y = 6 - 4 \cdot 1$

$x = 1$

Simplify the right side.

Simplify $6 - 4 \cdot 1$ .

Multiply $- 4$ by $1$ .

$y = 6 - 4$

$x = 1$

Subtract $4$ from $6$ .

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

Step 5

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

$(1, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Step 7

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

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