Solve by Substitution y=x-2 , y=4x+1

$y = x - 2$ , $y = 4 x + 1$

Step 1

Eliminate the equal sides of each equation and combine.

$x - 2 = 4 x + 1$

Step 2

Solve $x - 2 = 4 x + 1$ for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$x - 2 - 4 x = 1$

Subtract $4 x$ from $x$ .

$- 3 x - 2 = 1$

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

Add $2$ to both sides of the equation.

$- 3 x = 1 + 2$

Add $1$ and $2$ .

$- 3 x = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $3$ by $- 3$ .

$x = - 1$

Step 3

Evaluate $y$ when $x = - 1$ .

Substitute $- 1$ for $x$ .

$y = 4 (- 1) + 1$

Simplify $4 (- 1) + 1$ .

Multiply $4$ by $- 1$ .

$y = - 4 + 1$

Add $- 4$ and $1$ .

$y = - 3$

Step 4

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

$(- 1, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, - 3)$

Equation Form:

$x = - 1, y = - 3$

Step 6

Solve by Substitution y=x-2 , y=4x+1

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