Algebra Examples

$[\begin{array}{c} x & y \\ x + y & x - y \end{array}] = [\begin{array}{c} 4 & - 5 \\ - 1 & 9 \end{array}]$

Step 1

Write as a linear system of equations.

$x = 4$

$y = - 5$

$x + y = - 1$

$x - y = 9$

Step 2

Solve the system of equations.

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Step 2.1

Replace all occurrences of $x$ with $4$ in each equation.

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Step 2.1.1

Replace all occurrences of $x$ in $x + y = - 1$ with $4$ .

$(4) + y = - 1$

$x = 4$

$y = - 5$

$x - y = 9$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Remove parentheses.

$4 + y = - 1$

$x = 4$

$y = - 5$

$x - y = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

$x - y = 9$

Step 2.1.3

Replace all occurrences of $x$ in $x - y = 9$ with $4$ .

$(4) - y = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

Step 2.1.4

Simplify the left side.

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Step 2.1.4.1

Remove parentheses.

$4 - y = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

$4 - y = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

$4 - y = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

Step 2.2

Replace all occurrences of $y$ with $- 5$ in each equation.

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Step 2.2.1

Replace all occurrences of $y$ in $4 - y = 9$ with $- 5$ .

$4 - (- 5) = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Simplify $4 - (- 5)$ .

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Step 2.2.2.1.1

Multiply $- 1$ by $- 5$ .

$4 + 5 = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

Step 2.2.2.1.2

Add $4$ and $5$ .

$9 = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

$9 = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

$9 = 9$

$4 + y = - 1$

$x = 4$

$y = - 5$

Step 2.2.3

Replace all occurrences of $y$ in $4 + y = - 1$ with $- 5$ .

$4 - 5 = - 1$

$9 = 9$

$x = 4$

$y = - 5$

Step 2.2.4

Simplify the left side.

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Step 2.2.4.1

Simplify $4 - 5$ .

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Step 2.2.4.1.1

Remove parentheses.

$4 - 5 = - 1$

$9 = 9$

$x = 4$

$y = - 5$

Step 2.2.4.1.2

Subtract $5$ from $4$ .

$- 1 = - 1$

$9 = 9$

$x = 4$

$y = - 5$

$- 1 = - 1$

$9 = 9$

$x = 4$

$y = - 5$

$- 1 = - 1$

$9 = 9$

$x = 4$

$y = - 5$

$- 1 = - 1$

$9 = 9$

$x = 4$

$y = - 5$

Step 2.3

Remove any equations from the system that are always true.

$x = 4$

$y = - 5$

Step 2.4

List all of the solutions.

$x = 4, y = - 5$