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Determine the coordinates of the intercept of the following two lines: $2x - 3y = 17$ and $3x - y = 15$

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The coordinates of the intercept of the following two lines: $2x - 3y = 17$ and $3x - y = 15$ is the point where $x$ and $y$ are equal in both equations.

To determine the coordinates we solve the two equations simultaneously.

$2x-3y=17$

$3x-y=15$

Make $y$ subject of formula in the second equation

$y=3x-15$

Substituting for $y$ in the 1st equation becomes:

$2x-3(3x-15)=17$

$2x-9x+45=17$

$x=\dfrac{17-45}{-7}= 4$

Since we already know that $y=3x-15$, we can determine the value of $x$

$4=3x-15$

$x=\dfrac{19}{3}$
by Wooden (4,853 points)

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