Linear Algebra Examples

$2 x + y = 6$ , $6 x = - 3 y + 12$

Step 1

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

$y = 6 - 2 x$

$6 x = - 3 y + 12$

Step 2

Replace all occurrences of $y$ with $6 - 2 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $6 x = - 3 y + 12$ with $6 - 2 x$ .

$6 x = - 3 (6 - 2 x) + 12$

$y = 6 - 2 x$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 3 (6 - 2 x) + 12$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$6 x = - 3 \cdot 6 - 3 (- 2 x) + 12$

$y = 6 - 2 x$

Step 2.2.1.1.2

Multiply $- 3$ by $6$ .

$6 x = - 18 - 3 (- 2 x) + 12$

$y = 6 - 2 x$

Step 2.2.1.1.3

Multiply $- 2$ by $- 3$ .

$6 x = - 18 + 6 x + 12$

$y = 6 - 2 x$

$6 x = - 18 + 6 x + 12$

$y = 6 - 2 x$

Step 2.2.1.2

Add $- 18$ and $12$ .

$6 x = 6 x - 6$

$y = 6 - 2 x$

$6 x = 6 x - 6$

$y = 6 - 2 x$

$6 x = 6 x - 6$

$y = 6 - 2 x$

$6 x = 6 x - 6$

$y = 6 - 2 x$

Step 3

Solve for $x$ in $6 x = 6 x - 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $6 x$ from both sides of the equation.

$6 x - 6 x = - 6$

$y = 6 - 2 x$

Step 3.1.2

Subtract $6 x$ from $6 x$ .

$0 = - 6$

$y = 6 - 2 x$

$0 = - 6$

$y = 6 - 2 x$

Step 3.2

Since $0 \neq - 6$ , there are no solutions.

No solution

$y = 6 - 2 x$

No solution

Step 4