Find the Points of Intersection 3x-6y=12 4x-8y=16

$3 x - 6 y = 12$ $4 x - 8 y = 16$

Step 1

Solve for $x$ in $3 x - 6 y = 12$ .

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

$3 x = 12 + 6 y$

$4 x - 8 y = 16$

Divide each term in $3 x = 12 + 6 y$ by $3$ and simplify.

Divide each term in $3 x = 12 + 6 y$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3} + \frac{6 y}{3}$

$4 x - 8 y = 16$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3} + \frac{6 y}{3}$

$4 x - 8 y = 16$

Divide $x$ by $1$ .

$x = \frac{12}{3} + \frac{6 y}{3}$

$4 x - 8 y = 16$

$x = \frac{12}{3} + \frac{6 y}{3}$

$4 x - 8 y = 16$

$x = \frac{12}{3} + \frac{6 y}{3}$

$4 x - 8 y = 16$

Simplify the right side.

Simplify each term.

Divide $12$ by $3$ .

$x = 4 + \frac{6 y}{3}$

$4 x - 8 y = 16$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 y$ .

$x = 4 + \frac{3 (2 y)}{3}$

$4 x - 8 y = 16$

Cancel the common factors.

Factor $3$ out of $3$ .

$x = 4 + \frac{3 (2 y)}{3 (1)}$

$4 x - 8 y = 16$

Cancel the common factor.

$x = 4 + \frac{3 (2 y)}{3 \cdot 1}$

$4 x - 8 y = 16$

Rewrite the expression.

$x = 4 + \frac{2 y}{1}$

$4 x - 8 y = 16$

Divide $2 y$ by $1$ .

$x = 4 + 2 y$

$4 x - 8 y = 16$

$x = 4 + 2 y$

$4 x - 8 y = 16$

$x = 4 + 2 y$

$4 x - 8 y = 16$

$x = 4 + 2 y$

$4 x - 8 y = 16$

$x = 4 + 2 y$

$4 x - 8 y = 16$

$x = 4 + 2 y$

$4 x - 8 y = 16$

$x = 4 + 2 y$

$4 x - 8 y = 16$

Step 2

Replace all occurrences of $x$ with $4 + 2 y$ in each equation.

Replace all occurrences of $x$ in $4 x - 8 y = 16$ with $4 + 2 y$ .

$4 (4 + 2 y) - 8 y = 16$

$x = 4 + 2 y$

Simplify the left side.

Simplify $4 (4 + 2 y) - 8 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 4 + 4 (2 y) - 8 y = 16$

$x = 4 + 2 y$

Multiply $4$ by $4$ .

$16 + 4 (2 y) - 8 y = 16$

$x = 4 + 2 y$

Multiply $2$ by $4$ .

$16 + 8 y - 8 y = 16$

$x = 4 + 2 y$

$16 + 8 y - 8 y = 16$

$x = 4 + 2 y$

Combine the opposite terms in $16 + 8 y - 8 y$ .

Subtract $8 y$ from $8 y$ .

$16 + 0 = 16$

$x = 4 + 2 y$

Add $16$ and $0$ .

$16 = 16$

$x = 4 + 2 y$

$16 = 16$

$x = 4 + 2 y$

$16 = 16$

$x = 4 + 2 y$

$16 = 16$

$x = 4 + 2 y$

$16 = 16$

$x = 4 + 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 + 2 y$

Step 4

Find the Points of Intersection 3x-6y=12 4x-8y=16

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