Question

solve the following system of equations.
$5x + 3y = 5$
$5x + 7y = 25$
$x = $
$y = $

Explanation:

Step1: Subtract the first equation from the second equation to eliminate \(x\).

The two equations are:

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Subtract equation \((1)\) from equation \((2)\):

$$ (5x + 7y)-(5x + 3y)=25 - 5 $$

Simplify the left - hand side and the right - hand side:

$$ 5x+7y - 5x - 3y=20 $$

$$ 4y = 20 $$

Step2: Solve for \(y\).

Divide both sides of the equation \(4y = 20\) by \(4\):

$$ y=\frac{20}{4}=5 $$

Step3: Substitute \(y = 5\) into the first equation to solve for \(x\).

Substitute \(y = 5\) into \(5x+3y = 5\):

$$ 5x+3\times5 = 5 $$

$$ 5x+15 = 5 $$

Subtract \(15\) from both sides:

$$ 5x=5 - 15 $$

$$ 5x=- 10 $$

Divide both sides by \(5\):

$$ x=\frac{-10}{5}=-2 $$

Answer:

\(x=-2\), \(y = 5\)