Find the Points of Intersection 2x+3y=30 2x+y=26

$2 x + 3 y = 30$ $2 x + y = 26$

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 26 - 2 x$

$2 x + 3 y = 30$

Step 2

Replace all occurrences of $y$ with $26 - 2 x$ in each equation.

Replace all occurrences of $y$ in $2 x + 3 y = 30$ with $26 - 2 x$ .

$2 x + 3 (26 - 2 x) = 30$

$y = 26 - 2 x$

Simplify the left side.

Simplify $2 x + 3 (26 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$2 x + 3 \cdot 26 + 3 (- 2 x) = 30$

$y = 26 - 2 x$

Multiply $3$ by $26$ .

$2 x + 78 + 3 (- 2 x) = 30$

$y = 26 - 2 x$

Multiply $- 2$ by $3$ .

$2 x + 78 - 6 x = 30$

$y = 26 - 2 x$

$2 x + 78 - 6 x = 30$

$y = 26 - 2 x$

Subtract $6 x$ from $2 x$ .

$- 4 x + 78 = 30$

$y = 26 - 2 x$

$- 4 x + 78 = 30$

$y = 26 - 2 x$

$- 4 x + 78 = 30$

$y = 26 - 2 x$

$- 4 x + 78 = 30$

$y = 26 - 2 x$

Step 3

Solve for $x$ in $- 4 x + 78 = 30$ .

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

Subtract $78$ from both sides of the equation.

$- 4 x = 30 - 78$

$y = 26 - 2 x$

Subtract $78$ from $30$ .

$- 4 x = - 48$

$y = 26 - 2 x$

$- 4 x = - 48$

$y = 26 - 2 x$

Divide each term in $- 4 x = - 48$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 48$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 48}{- 4}$

$y = 26 - 2 x$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 48}{- 4}$

$y = 26 - 2 x$

Divide $x$ by $1$ .

$x = \frac{- 48}{- 4}$

$y = 26 - 2 x$

$x = \frac{- 48}{- 4}$

$y = 26 - 2 x$

$x = \frac{- 48}{- 4}$

$y = 26 - 2 x$

Simplify the right side.

Divide $- 48$ by $- 4$ .

$x = 12$

$y = 26 - 2 x$

$x = 12$

$y = 26 - 2 x$

$x = 12$

$y = 26 - 2 x$

$x = 12$

$y = 26 - 2 x$

Step 4

Replace all occurrences of $x$ with $12$ in each equation.

Replace all occurrences of $x$ in $y = 26 - 2 x$ with $12$ .

$y = 26 - 2 \cdot 12$

$x = 12$

Simplify the right side.

Simplify $26 - 2 \cdot 12$ .

Multiply $- 2$ by $12$ .

$y = 26 - 24$

$x = 12$

Subtract $24$ from $26$ .

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

Step 5

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

$(12, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(12, 2)$

Equation Form:

$x = 12, y = 2$

Step 7

Find the Points of Intersection 2x+3y=30 2x+y=26

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