Algebra Examples

$3 x + 6 y = 27$ $x + 2 y = 11$

Step 1

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$3 x + 6 y = 27$

$(- 3) \cdot (x + 2 y) = (- 3) (11)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(- 3) \cdot (x + 2 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$3 x + 6 y = 27$

$- 3 x - 3 (2 y) = (- 3) (11)$

Step 2.1.1.2

Multiply $2$ by $- 3$ .

$3 x + 6 y = 27$

$- 3 x - 6 y = (- 3) (11)$

$3 x + 6 y = 27$

$- 3 x - 6 y = (- 3) (11)$

$3 x + 6 y = 27$

$- 3 x - 6 y = (- 3) (11)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 3$ by $11$ .

$3 x + 6 y = 27$

$- 3 x - 6 y = - 33$

$3 x + 6 y = 27$

$- 3 x - 6 y = - 33$

$3 x + 6 y = 27$

$- 3 x - 6 y = - 33$

Step 3

Add the two equations together to eliminate $x$ from the system.

Step 4

Since $0 \neq - 6$ , there are no solutions.

No solution

Step 5