Solve by Substitution 2x-y=16 , 3x+y=24

$2 x - y = 16$ , $3 x + y = 24$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = 24 - 3 x$

$2 x - y = 16$

Step 2

Replace all occurrences of $y$ with $24 - 3 x$ in each equation.

Replace all occurrences of $y$ in $2 x - y = 16$ with $24 - 3 x$ .

$2 x - (24 - 3 x) = 16$

$y = 24 - 3 x$

Simplify the left side.

Simplify $2 x - (24 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$2 x - 1 \cdot 24 - (- 3 x) = 16$

$y = 24 - 3 x$

Multiply $- 1$ by $24$ .

$2 x - 24 - (- 3 x) = 16$

$y = 24 - 3 x$

Multiply $- 3$ by $- 1$ .

$2 x - 24 + 3 x = 16$

$y = 24 - 3 x$

$2 x - 24 + 3 x = 16$

$y = 24 - 3 x$

Add $2 x$ and $3 x$ .

$5 x - 24 = 16$

$y = 24 - 3 x$

$5 x - 24 = 16$

$y = 24 - 3 x$

$5 x - 24 = 16$

$y = 24 - 3 x$

$5 x - 24 = 16$

$y = 24 - 3 x$

Step 3

Solve for $x$ in $5 x - 24 = 16$ .

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

Add $24$ to both sides of the equation.

$5 x = 16 + 24$

$y = 24 - 3 x$

Add $16$ and $24$ .

$5 x = 40$

$y = 24 - 3 x$

$5 x = 40$

$y = 24 - 3 x$

Divide each term in $5 x = 40$ by $5$ and simplify.

Divide each term in $5 x = 40$ by $5$ .

$\frac{5 x}{5} = \frac{40}{5}$

$y = 24 - 3 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{40}{5}$

$y = 24 - 3 x$

Divide $x$ by $1$ .

$x = \frac{40}{5}$

$y = 24 - 3 x$

$x = \frac{40}{5}$

$y = 24 - 3 x$

$x = \frac{40}{5}$

$y = 24 - 3 x$

Simplify the right side.

Divide $40$ by $5$ .

$x = 8$

$y = 24 - 3 x$

$x = 8$

$y = 24 - 3 x$

$x = 8$

$y = 24 - 3 x$

$x = 8$

$y = 24 - 3 x$

Step 4

Replace all occurrences of $x$ with $8$ in each equation.

Replace all occurrences of $x$ in $y = 24 - 3 x$ with $8$ .

$y = 24 - 3 \cdot 8$

$x = 8$

Simplify the right side.

Simplify $24 - 3 \cdot 8$ .

Multiply $- 3$ by $8$ .

$y = 24 - 24$

$x = 8$

Subtract $24$ from $24$ .

$y = 0$

$x = 8$

$y = 0$

$x = 8$

$y = 0$

$x = 8$

$y = 0$

$x = 8$

Step 5

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

$(8, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, 0)$

Equation Form:

$x = 8, y = 0$

Step 7

Solve by Substitution 2x-y=16 , 3x+y=24

Related Questions

Support LCMGCF.com by disabling your adblocker.