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Note: The answer printed in the book is given as $({\frac {7}{8}},{\frac {11}{8}})$. This is incorrect!

If the two lines $y_{1}=-2x+5,\,$ and $y_{2}=5x-3\,$ intersect, then $y_{1}=y_{2}\,$. Therefore:

$y_{1}-y_{2}=(-2x+5)-(5x-3)=0\,$

$-7x+8=0\,$

$-7x=-8\,$

$x={\frac {8}{7}}$

Thus, we can now plug in the value for x into any one of our two equations to find the point of interception:

$y_{2}=5\cdot {\frac {8}{7}}-3={\frac {40}{7}}-3={\frac {19}{7}}$

Thus, the point of interception is $\left({\frac {8}{7}},{\frac {19}{7}}\right)$.