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

You have to solve equation system: { y = 3 x + 4 y = 2 x + 6 ∣ ∗ ( − 1 ) ​ { y = 3 x + 4 − y = − 2 x − 6 ​ 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.

Answered by marmal | 2024-06-10

Answer:
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**
Step-by-step 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)

Answered by lidaralbany | 2024-06-12

The x-coordinate of the intersection point of the lines y = 2 x + 6 and y = 3 x + 4 is 2. This was found by setting the two equations equal to each other and solving for x. The intersection point is ( 2 , 10 ) .
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Answered by marmal | 2024-10-22