Algebra Examples

$[\begin{array}{c} 3 x \\ y + 4 \end{array}] = [\begin{array}{c} y + 8 \\ 17 \end{array}]$

Step 1

The matrix equation can be written as a set of equations.

$3 x = y + 8$

$y + 4 = 17$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$y = 17 - 4$

$3 x = y + 8$

Step 2.2

Subtract $4$ from $17$ .

$y = 13$

$3 x = y + 8$

$y = 13$

$3 x = y + 8$

Step 3

Replace all occurrences of $y$ with $13$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $3 x = y + 8$ with $13$ .

$3 x = (13) + 8$

$y = 13$

Step 3.2

Simplify the right side.

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Step 3.2.1

Add $13$ and $8$ .

$3 x = 21$

$y = 13$

$3 x = 21$

$y = 13$

$3 x = 21$

$y = 13$

Step 4

Divide each term in $3 x = 21$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = 21$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3}$

$y = 13$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3}$

$y = 13$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{3}$

$y = 13$

$x = \frac{21}{3}$

$y = 13$

$x = \frac{21}{3}$

$y = 13$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $21$ by $3$ .

$x = 7$

$y = 13$

$x = 7$

$y = 13$

$x = 7$

$y = 13$

Step 5

Solve the system of equations.

$x = 7 y = 13$

Step 6

List all of the solutions.

$x = 7, y = 13$