# Show that 2x+3y=10 and 4x+6y=5 will never intersect

2
by DashieXp

2016-06-27T20:28:19+08:00
You can find the point of intersection of the two lines

by plotting, assume any no. for example 1st equation , the value of x, then you will have your y value..do it same, to equation two, let us see if they intersect in the origin, because when we are going to equate each other,the 2 variables  become zero..
oh , they don't actually meet, becasue they are parallel to each other...sorry
the solution is a couple of numbers, since they are both the same, that is why if you plot the two, u will have a parallel line.the solution is 2x+3y=10
• Brainly User
2016-07-03T23:40:40+08:00
Solution:  Find the slopes.  If the system have exactly the same slope, but different y-intercepts, then they are parallel, and their graphs do not intersect.

Equation 1:
2x + 3y = 10
3y = -2x + 10
3y/3 = -2x/3 + 10/3

y = -2x/3 + 10/3
m (slope) = -2/3     y-intercept = 10/3

Equation 2:
4x + 6y = 5
6y = -4x + 5
6y/6 = -4x/6 + 5/6

y = -2x/3 + 5/6
m (slope) = -2/3              y-intercept = 5/6