# How do you find the solution of the system of equations 3x+5y=7 and 5x+9y=7?

May 15, 2015

First isolate the same term on one side of both equations.

Let us target $y$. If we multiply the first equation by $9$ and the second by $5$ we get:

$27 x + 45 y = 63$ and $25 x + 45 y = 35$

Subtract $27 x$ from both sides of the first equation and $25 x$ from both sides of the second to get:

$45 y = 63 - 27 x$ and $45 y = 35 - 25 x$

So $63 - 27 x = 45 y = 35 - 25 x$

Ignore the $45 y$ in the middle and add 27x to both sides to get

$63 = 35 + 2 x$

Subtract $35$ from both sides to get

$28 = 2 x$

Divide by 2 to get $x = 14$

Then $45 y = 35 - 25 x = 35 - 25 \cdot 14 = 35 - 350 = - 315$

Divide both sides by 45 to get

$y = - \frac{315}{45} = - 7$

May 15, 2015

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