$\"\"$

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Elimination method:

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Given equations are,

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$\"\"$ ----------(1)

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$\"\"$ ----------(2)

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First equation has multiply each side by 3.

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$\"\"$ (First equation)

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$\"\"$ (Apply zero property: $\"\"$ )

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$\"\"$ (Apply distributive property: $\"\"$ )

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$\"\"$ (Multiply: $\"\"$ )

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$\"\"$ --------(3) $\"\"$

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Second equation has multiply each side by 2.

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$\"\"$ (Second equation)

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$\"\"$

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$\"\"$ (Apply distributive property: $\"\"$ )

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$\"\"$ -------(4) (Multiply: $\"\"$ )

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(3) and (4) equations when the coefficients of a variable $\"\"$ and $\"\"$ are same,

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subtracting the equations will eliminate the variable. $\"\"$

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Subtracting (4) and (3) equations will eliminate the variable y.

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$\"\"$ (Subtracting (4) and (3) equations)

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Apply division property of equality: If a = b then $\"\"$ .

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$\"\"$ (Divide each side by 32)

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$\"\"$ (Cancel common terms)

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$\"\"$ (Divide: $\"\"$ ) $\"\"$

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Substitute $\"\"$ for x in either equation to find y.

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$\"\"$ (Second equation)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Multiply: $\"\"$ )

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Apply commutative property of addition: $\"\"$ .

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$\"\"$ $\"\"$

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$\"\"$ (Subtract 5 from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Apply additive identity property: $\"\"$ )

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$\"\"$ (Subtract: $\"\"$ )

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$\"\"$ (Divide each side by 3)

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$\"\"$ (Cancel common terms) $\"\"$

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Check the solution:

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To Check, substitute $\"\"$ and $\"\"$ in either equation.

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$\"\"$ (First equation)

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$\"\"$ (Substitute $\"\"$ and $\"\"$ )

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$\"\"$ (Multiply: $\"\"$ )

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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The solution $\"\"$ is true. $\"\"$

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The solution is $\"\"$ .