Solve by Substitution 9x+y=21 -x-3=y

$9 x + y = 21$ $- x - 3 = y$

Step 1

Subtract $9 x$ from both sides of the equation.

$y = 21 - 9 x$

$- x - 3 = y$

Step 2

Replace all occurrences of $y$ with $21 - 9 x$ in each equation.

Replace all occurrences of $y$ in $- x - 3 = y$ with $21 - 9 x$ .

$- x - 3 = 21 - 9 x$

$y = 21 - 9 x$

Simplify the left side.

Remove parentheses.

$- x - 3 = 21 - 9 x$

$y = 21 - 9 x$

$- x - 3 = 21 - 9 x$

$y = 21 - 9 x$

$- x - 3 = 21 - 9 x$

$y = 21 - 9 x$

Step 3

Solve for $x$ in $- x - 3 = 21 - 9 x$ .

Move all terms containing $x$ to the left side of the equation.

Add $9 x$ to both sides of the equation.

$- x - 3 + 9 x = 21$

$y = 21 - 9 x$

Add $- x$ and $9 x$ .

$8 x - 3 = 21$

$y = 21 - 9 x$

$8 x - 3 = 21$

$y = 21 - 9 x$

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

Add $3$ to both sides of the equation.

$8 x = 21 + 3$

$y = 21 - 9 x$

Add $21$ and $3$ .

$8 x = 24$

$y = 21 - 9 x$

$8 x = 24$

$y = 21 - 9 x$

Divide each term in $8 x = 24$ by $8$ and simplify.

Divide each term in $8 x = 24$ by $8$ .

$\frac{8 x}{8} = \frac{24}{8}$

$y = 21 - 9 x$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{24}{8}$

$y = 21 - 9 x$

Divide $x$ by $1$ .

$x = \frac{24}{8}$

$y = 21 - 9 x$

$x = \frac{24}{8}$

$y = 21 - 9 x$

$x = \frac{24}{8}$

$y = 21 - 9 x$

Simplify the right side.

Divide $24$ by $8$ .

$x = 3$

$y = 21 - 9 x$

$x = 3$

$y = 21 - 9 x$

$x = 3$

$y = 21 - 9 x$

$x = 3$

$y = 21 - 9 x$

Step 4

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

Replace all occurrences of $x$ in $y = 21 - 9 x$ with $3$ .

$y = 21 - 9 \cdot 3$

$x = 3$

Simplify the right side.

Simplify $21 - 9 \cdot 3$ .

Multiply $- 9$ by $3$ .

$y = 21 - 27$

$x = 3$

Subtract $27$ from $21$ .

$y = - 6$

$x = 3$

$y = - 6$

$x = 3$

$y = - 6$

$x = 3$

$y = - 6$

$x = 3$

Step 5

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

$(3, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, - 6)$

Equation Form:

$x = 3, y = - 6$

Step 7

Solve by Substitution 9x+y=21 -x-3=y

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