Find the equation of straight line passing through the intersection of the lines 5x-2y-12=0 and 4x-7y-15=0 and parallel to the line 3x-2y+5=0

Dear Student

The intersection point of two lines can be calculated by solving the linear equation of both lines .
By solving given equations, we will get
x=2
y= –1

The line parallel to line ax+by+c=0 is given by ax+by+d=0
so line equation will be 3x –2y + d=0
since line passes through (2,-1)
3 x 2 –2 x (-1) +d=0
d= –8
so , The equation of line is 3x-2y-8=0

Thanks