Solve the Matrix Equation [[5x],[14]]=[[4+x],[2y-2]]

$[\begin{array}{c} 5 x \\ 14 \end{array}] = [\begin{array}{c} 4 + x \\ 2 y - 2 \end{array}]$

Step 1

Rearrange $4 + x$ .

$[\begin{array}{c} 5 x \\ 14 \end{array}] = [\begin{array}{c} x + 4 \\ 2 y - 2 \end{array}]$

Step 2

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

$5 x = x + 4$

$14 = 2 y - 2$

Step 3

Solve for $x$ in $5 x = x + 4$ .

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

Subtract $x$ from both sides of the equation.

$5 x - x = 4$

$14 = 2 y - 2$

Subtract $x$ from $5 x$ .

$4 x = 4$

$14 = 2 y - 2$

$4 x = 4$

$14 = 2 y - 2$

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

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

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

$14 = 2 y - 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

$14 = 2 y - 2$

Divide $x$ by $1$ .

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

$14 = 2 y - 2$

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

$14 = 2 y - 2$

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

$14 = 2 y - 2$

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

$14 = 2 y - 2$

$x = 1$

$14 = 2 y - 2$

$x = 1$

$14 = 2 y - 2$

$x = 1$

$14 = 2 y - 2$

Step 4

Replace all occurrences of $x$ with $1$ in each equation.

Rewrite the equation as $2 y - 2 = 14$ .

$2 y - 2 = 14$

$x = 1$

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

Add $2$ to both sides of the equation.

$2 y = 14 + 2$

$x = 1$

Add $14$ and $2$ .

$2 y = 16$

$x = 1$

$2 y = 16$

$x = 1$

Divide each term in $2 y = 16$ by $2$ and simplify.

Divide each term in $2 y = 16$ by $2$ .

$\frac{2 y}{2} = \frac{16}{2}$

$x = 1$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{16}{2}$

$x = 1$

Divide $y$ by $1$ .

$y = \frac{16}{2}$

$x = 1$

$y = \frac{16}{2}$

$x = 1$

$y = \frac{16}{2}$

$x = 1$

Simplify the right side.

Divide $16$ by $2$ .

$y = 8$

$x = 1$

$y = 8$

$x = 1$

$y = 8$

$x = 1$

$y = 8$

$x = 1$

Step 5

List all of the solutions.

$y = 8, x = 1$

Solve the Matrix Equation [[5x],[14]]=[[4+x],[2y-2]]

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