Linear Algebra Examples

$y = x + 3$ , $y = 2 x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$x + 3 = 2 x - 1$

Step 2

Solve $x + 3 = 2 x - 1$ for $x$ .

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Subtract $2 x$ from both sides of the equation.

$x + 3 - 2 x = - 1$

Step 2.1.2

Subtract $2 x$ from $x$ .

$- x + 3 = - 1$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $3$ from both sides of the equation.

$- x = - 1 - 3$

Step 2.2.2

Subtract $3$ from $- 1$ .

$- x = - 4$

Step 2.3

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide $- 4$ by $- 1$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Tap for more steps...

Step 3.1

Substitute $4$ for $x$ .

$y = 2 (4) - 1$

Step 3.2

Simplify $2 (4) - 1$ .

Tap for more steps...

Step 3.2.1

Multiply $2$ by $4$ .

$y = 8 - 1$

Step 3.2.2

Subtract $1$ from $8$ .

$y = 7$

Step 4

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

$(4, 7)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 7)$

Equation Form:

$x = 4, y = 7$

Step 6