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

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Answer 1 · 2015-05-15T21:17:42

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

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

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

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

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

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

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

$63 = 35 + 2 x$ $63=35+2x$

Subtract $35$ $35$ from both sides to get

$28 = 2 x$ $28=2x$

Divide by 2 to get $x = 14$ $x=14$

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

Divide both sides by 45 to get

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

Answer 2 · 2015-05-15T21:18:59

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How do you find the solution of the system of equations 3x+5y=73x+5y=73x+5y=7 and 5x+9y=75x+9y=75x+9y=7?