Find the solutions of the form x=a, y=0and x=0, y=b for the following equations: 2x+5y=10 and 2x+3y=6. is there any common solution?

see explanation

Step-by-step explanation:

To find the intercepts, that is where the graph of the lines cross the x and y axes.

• let x = 0, in the equation for y-intercept

• let y = 0, in the equation for x-intercept

Consider each equation separately

2x + 5y = 10

x = 0 : 5y = 10 ⇒ y = 2 ⇒ (0, 2) ← y - intercept

y = 0 : 2x = 10 ⇒ x = 5 ⇒ (5, 0) ← x - intercept

2x + 3y = 6

x = 0 : 3y = 6 ⇒ y = 2 ⇒ (0, 2) ← y - intercept

y = 0 : 2x = 6 ⇒ x = 3 ⇒ (3, 0) ← x - intercept

The common solution is the y-intercept in both equations (0, 2)