Question

What type of straight lines will be represented by the system of equations 2x +
3y =5 and 4x + y = 7 ?​

Answer 1

Intersecting lines

Step-by-step explanation:

Equation 1: 2x +3y = 5 or 2x +3y -5 = 0.

Equation 2: 4x + y = 7 or 4x + y -7 = 0.

a1 = 2, b1 = 3, c1 = -5

a2 = 4, b2 = 1, c2 = -7

$\frac{a1}{b1} = \frac{2}{3} \: \: \: \: \: and \: \: \: \frac{a2}{b2} = \frac{3}{1} = 3$

$so \: \: \: \frac{a1}{b1} ≠\: \frac{a2}{b2}$

So, the lines have unique solutions and therefore the lines are intersecting.