Solve by Substitution y=4x-9 , y=x-3

$y = 4 x - 9$ , $y = x - 3$

Step 1

Eliminate the equal sides of each equation and combine.

$4 x - 9 = x - 3$

Step 2

Solve $4 x - 9 = x - 3$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$4 x - 9 - x = - 3$

Subtract $x$ from $4 x$ .

$3 x - 9 = - 3$

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

Add $9$ to both sides of the equation.

$3 x = - 3 + 9$

Add $- 3$ and $9$ .

$3 x = 6$

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

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

$y = (2) - 3$

Substitute $2$ for $x$ in $y = (2) - 3$ and solve for $y$ .

Remove parentheses.

$y = 2 - 3$

Remove parentheses.

$y = (2) - 3$

Subtract $3$ from $2$ .

$y = - 1$

Step 4

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

$(2, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 6

Solve by Substitution y=4x-9 , y=x-3

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