Question 1049400
At that point,
{{{5x=y/2}}}<--->{{{y=10x}}} ,
{{{5x=z+2}}}<--->{{{z=5x-2}}} , and
{{{10x-7y+3z+24=0}}} .
That is a system of linear equations.
You can easily solve it by substitution.
Substituting {{{10x}}} for {{{y}}} , and {{{5x-2}}} for {{{z}}} in the long equation, you get
{{{10x-7(10x)+3(5x-2)+24=0}}}
{{{20x-70x+25x-6+24=0}}}
{{{-45x+18=0}}}
{{{18=45x}}}
{{{x=18/45}}}
{{{highlight(x=2/5)}}} .
Then {{{y=20(2/5)}}} , so {{{highlight(y=4)}}} , and
{{{z=5*(2/5)-2}}} , so {{{z=2-2}}}, and {{{highlight(z=0)}}} .
You can say that the point where the line crosses the plane is (2/5,4,0) .