Which statement is correct for (2x+5y=1) and (3x+7y=4)?

Lines intersect at one point

Two linear equations in two variables usually represent two lines. If the lines have different slopes, they meet at exactly one point, producing one unique ordered pair that satisfies both equations. In coefficient form, unequal ratios of the x- and y-coefficients indicate different slopes. Equal ratios of all corresponding coefficients would instead indicate coincident lines, while equal coefficient ratios with a different constant ratio would indicate parallel lines.

For 
m 2x+5y=1
m and 
m 3x+7y=4
m, compare the coefficient ratios: 
m 2/3
m is not equal to 
m 5/7
m. Thus the slopes are different, so the lines intersect at one point. For an additional check, elimination gives 
m 6x+15y=3
m and 
m 6x+14y=8
m; subtracting yields 
m y=-5
m and then 
m x=13
m. Hence option C is correct.

This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.