Linear Algebra Examples

$6 x + 3 y = 24$ , $4 x + 2 y = - 26$

Step 1

Solve for $x$ in $6 x + 3 y = 24$ .

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Step 1.1

Subtract $3 y$ from both sides of the equation.

$6 x = 24 - 3 y$

$4 x + 2 y = - 26$

Step 1.2

Divide each term in $6 x = 24 - 3 y$ by $6$ and simplify.

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Step 1.2.1

Divide each term in $6 x = 24 - 3 y$ by $6$ .

$\frac{6 x}{6} = \frac{24}{6} + \frac{- 3 y}{6}$

$4 x + 2 y = - 26$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $6$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{24}{6} + \frac{- 3 y}{6}$

$4 x + 2 y = - 26$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{6} + \frac{- 3 y}{6}$

$4 x + 2 y = - 26$

$x = \frac{24}{6} + \frac{- 3 y}{6}$

$4 x + 2 y = - 26$

$x = \frac{24}{6} + \frac{- 3 y}{6}$

$4 x + 2 y = - 26$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $24$ by $6$ .

$x = 4 + \frac{- 3 y}{6}$

$4 x + 2 y = - 26$

Step 1.2.3.1.2

Cancel the common factor of $- 3$ and $6$ .

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Step 1.2.3.1.2.1

Factor $3$ out of $- 3 y$ .

$x = 4 + \frac{3 (- y)}{6}$

$4 x + 2 y = - 26$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $3$ out of $6$ .

$x = 4 + \frac{3 (- y)}{3 (2)}$

$4 x + 2 y = - 26$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = 4 + \frac{3 (- y)}{3 \cdot 2}$

$4 x + 2 y = - 26$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = 4 + \frac{- y}{2}$

$4 x + 2 y = - 26$

$x = 4 + \frac{- y}{2}$

$4 x + 2 y = - 26$

$x = 4 + \frac{- y}{2}$

$4 x + 2 y = - 26$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = 4 - \frac{y}{2}$

$4 x + 2 y = - 26$

$x = 4 - \frac{y}{2}$

$4 x + 2 y = - 26$

$x = 4 - \frac{y}{2}$

$4 x + 2 y = - 26$

$x = 4 - \frac{y}{2}$

$4 x + 2 y = - 26$

$x = 4 - \frac{y}{2}$

$4 x + 2 y = - 26$

Step 2

Replace all occurrences of $x$ with $4 - \frac{y}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $4 x + 2 y = - 26$ with $4 - \frac{y}{2}$ .

$4 (4 - \frac{y}{2}) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (4 - \frac{y}{2}) + 2 y$ .

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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.

$4 \cdot 4 + 4 (- \frac{y}{2}) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.1.2

Multiply $4$ by $4$ .

$16 + 4 (- \frac{y}{2}) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

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Step 2.2.1.1.3.1

Move the leading negative in $- \frac{y}{2}$ into the numerator.

$16 + 4 (\frac{- y}{2}) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.1.3.2

Factor $2$ out of $4$ .

$16 + 2 (2) (\frac{- y}{2}) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.1.3.3

Cancel the common factor.

$16 + 2 \cdot (2 (\frac{- y}{2})) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.1.3.4

Rewrite the expression.

$16 + 2 (- y) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

$16 + 2 (- y) + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.1.4

Multiply $- 1$ by $2$ .

$16 - 2 y + 2 y = - 26$

$x = 4 - \frac{y}{2}$

$16 - 2 y + 2 y = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.2

Combine the opposite terms in $16 - 2 y + 2 y$ .

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Step 2.2.1.2.1

Add $- 2 y$ and $2 y$ .

$16 + 0 = - 26$

$x = 4 - \frac{y}{2}$

Step 2.2.1.2.2

Add $16$ and $0$ .

$16 = - 26$

$x = 4 - \frac{y}{2}$

$16 = - 26$

$x = 4 - \frac{y}{2}$

$16 = - 26$

$x = 4 - \frac{y}{2}$

$16 = - 26$

$x = 4 - \frac{y}{2}$

$16 = - 26$

$x = 4 - \frac{y}{2}$

Step 3

Since $16 = - 26$ is not true, there is no solution.

No solution

Step 4