If the curve touches, but does not cross the straight line at the point , then the straight line is a tangent to the curve at this point, and hence the curve and the straight line have the same slope.
The slope of the straight line is 7.
The slope of the curve can be found by differentiating.
The slopes are equal when , so substituting this value leads to
The point is on both the straight line and the curve, and therefore substituting these values for and into the equation of the curve will yield a second equation in and .
Hence, there are two linear equations for and which can be solved simultaneously. Multiplying the second equation by 2 gives
Adding this equation to the first gives
Substituting this value of into the second equation gives
Therefore, the solution is , .