The coordinates of the point of intersection of the two lines is [tex](8,2)[/tex]
Explanation:
The two equations are [tex]$2 x-7 y=2$[/tex] and [tex]$4 x+5 y=42$[/tex]
To determine the point of intersection of the two lines, we shall the equations using elimination method.
Thus, multiplying the equation [tex]$2 x-7 y=2$[/tex] by -2, we have,
[tex]\begin{aligned}-4 x+14 y &=-4 \\ 4 x+5 y &=42 \end{aligned}$\\---------------------------\\[/tex]
[tex]19y=38[/tex]
[tex]y=2[/tex]
Substituting [tex]y=2[/tex] in the equation [tex]$2 x-7 y=2$[/tex], we get,
[tex]2x-7(2)=2[/tex]
[tex]2x-14=2[/tex]
Adding both sides by 14, we get,
[tex]2x=16[/tex]
Dividing both sides by 2, we get,
[tex]x=8[/tex]
Thus, the coordinates of the point of intersection of the two lines is [tex](8,2)[/tex]
