Solve by Substitution 3x+2y=16 , x=3y-2

$3 x + 2 y = 16$ , $x = 3 y - 2$

Step 1

Replace all occurrences of $x$ with $3 y - 2$ in each equation.

Replace all occurrences of $x$ in $3 x + 2 y = 16$ with $3 y - 2$ .

$3 (3 y - 2) + 2 y = 16$

$x = 3 y - 2$

Simplify the left side.

Simplify $3 (3 y - 2) + 2 y$ .

Simplify each term.

Apply the distributive property.

$3 (3 y) + 3 \cdot - 2 + 2 y = 16$

$x = 3 y - 2$

Multiply $3$ by $3$ .

$9 y + 3 \cdot - 2 + 2 y = 16$

$x = 3 y - 2$

Multiply $3$ by $- 2$ .

$9 y - 6 + 2 y = 16$

$x = 3 y - 2$

$9 y - 6 + 2 y = 16$

$x = 3 y - 2$

Add $9 y$ and $2 y$ .

$11 y - 6 = 16$

$x = 3 y - 2$

$11 y - 6 = 16$

$x = 3 y - 2$

$11 y - 6 = 16$

$x = 3 y - 2$

$11 y - 6 = 16$

$x = 3 y - 2$

Step 2

Solve for $y$ in $11 y - 6 = 16$ .

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

Add $6$ to both sides of the equation.

$11 y = 16 + 6$

$x = 3 y - 2$

Add $16$ and $6$ .

$11 y = 22$

$x = 3 y - 2$

$11 y = 22$

$x = 3 y - 2$

Divide each term in $11 y = 22$ by $11$ and simplify.

Divide each term in $11 y = 22$ by $11$ .

$\frac{11 y}{11} = \frac{22}{11}$

$x = 3 y - 2$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{22}{11}$

$x = 3 y - 2$

Divide $y$ by $1$ .

$y = \frac{22}{11}$

$x = 3 y - 2$

$y = \frac{22}{11}$

$x = 3 y - 2$

$y = \frac{22}{11}$

$x = 3 y - 2$

Simplify the right side.

Divide $22$ by $11$ .

$y = 2$

$x = 3 y - 2$

$y = 2$

$x = 3 y - 2$

$y = 2$

$x = 3 y - 2$

$y = 2$

$x = 3 y - 2$

Step 3

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

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

$x = 3 (2) - 2$

$y = 2$

Simplify the right side.

Simplify $3 (2) - 2$ .

Multiply $3$ by $2$ .

$x = 6 - 2$

$y = 2$

Subtract $2$ from $6$ .

$x = 4$

$y = 2$

$x = 4$

$y = 2$

$x = 4$

$y = 2$

$x = 4$

$y = 2$

Step 4

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

$(4, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 6

Solve by Substitution 3x+2y=16 , x=3y-2

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