Question

What is the x-coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y = 2x + 6 and y = 3x + 4 intersect?

Can you please explain with some details?

Answer 1

You have to solve equation system:

`\left \{ {{y=2x+6}|*(-1) \atop {y=3x+4}} \right. \\ \left \{ {{-y=-2x-6} \atop {y=3x+4}} \right. \\ 0=x-2\\ x=2`

Or you can also graph it. Look at enclose.
To graph it you have to draw two lines choosing two points for each one.
For example:
y=2x+6
so if x=0 y = 6
if x = 1 y = 8
You connect this points and you have y=2x+6 line. You do this the same with the second line.

Answer 2

The x-coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y = 2x + 6 and y = 3x + 4 intersect is:

x=2

Explanation:

The point of intersection of the two lines is the point where the y-value of the two lines are equal.

Now, in order to find the x-coordinate of the point of intersection we equate the equation of two lines in terms of x and by some operation we obtain the value of x.

Here the equation of two lines are:

y = 2x + 6 and y = 3x + 4

Now, on equating the y-value we have:

2x+6=3x+4

Now,

3x-2x=6-4

i.e.

x=2

Also, on putting the value of x in any of the two equation of lines we have:

y=10

Hence, the point of intersection is: (2,10)