Algebra Examples

$- 3 x - 8 y = 20$ , $- 5 x + y = 19$

Step 1

Add $5 x$ to both sides of the equation.

$y = 19 + 5 x$

$- 3 x - 8 y = 20$

Step 2

Replace all occurrences of $y$ with $19 + 5 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 3 x - 8 y = 20$ with $19 + 5 x$ .

$- 3 x - 8 (19 + 5 x) = 20$

$y = 19 + 5 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 x - 8 (19 + 5 x)$ .

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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.

$- 3 x - 8 \cdot 19 - 8 (5 x) = 20$

$y = 19 + 5 x$

Step 2.2.1.1.2

Multiply $- 8$ by $19$ .

$- 3 x - 152 - 8 (5 x) = 20$

$y = 19 + 5 x$

Step 2.2.1.1.3

Multiply $5$ by $- 8$ .

$- 3 x - 152 - 40 x = 20$

$y = 19 + 5 x$

$- 3 x - 152 - 40 x = 20$

$y = 19 + 5 x$

Step 2.2.1.2

Subtract $40 x$ from $- 3 x$ .

$- 43 x - 152 = 20$

$y = 19 + 5 x$

$- 43 x - 152 = 20$

$y = 19 + 5 x$

$- 43 x - 152 = 20$

$y = 19 + 5 x$

$- 43 x - 152 = 20$

$y = 19 + 5 x$

Step 3

Solve for $x$ in $- 43 x - 152 = 20$ .

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Step 3.1

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

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Step 3.1.1

Add $152$ to both sides of the equation.

$- 43 x = 20 + 152$

$y = 19 + 5 x$

Step 3.1.2

Add $20$ and $152$ .

$- 43 x = 172$

$y = 19 + 5 x$

$- 43 x = 172$

$y = 19 + 5 x$

Step 3.2

Divide each term in $- 43 x = 172$ by $- 43$ and simplify.

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Step 3.2.1

Divide each term in $- 43 x = 172$ by $- 43$ .

$\frac{- 43 x}{- 43} = \frac{172}{- 43}$

$y = 19 + 5 x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 43$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 43 x}{- 43} = \frac{172}{- 43}$

$y = 19 + 5 x$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{172}{- 43}$

$y = 19 + 5 x$

$x = \frac{172}{- 43}$

$y = 19 + 5 x$

$x = \frac{172}{- 43}$

$y = 19 + 5 x$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $172$ by $- 43$ .

$x = - 4$

$y = 19 + 5 x$

$x = - 4$

$y = 19 + 5 x$

$x = - 4$

$y = 19 + 5 x$

$x = - 4$

$y = 19 + 5 x$

Step 4

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

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Step 4.1

Replace all occurrences of $x$ in $y = 19 + 5 x$ with $- 4$ .

$y = 19 + 5 (- 4)$

$x = - 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $19 + 5 (- 4)$ .

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Step 4.2.1.1

Multiply $5$ by $- 4$ .

$y = 19 - 20$

$x = - 4$

Step 4.2.1.2

Subtract $20$ from $19$ .

$y = - 1$

$x = - 4$

$y = - 1$

$x = - 4$

$y = - 1$

$x = - 4$

$y = - 1$

$x = - 4$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 4, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Step 7