Answer:
option B
Step-by-step explanation:
Given :
![y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%20%2B%203%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B5%7D%7B2%7Dx%20%2B%20%5Cfrac%7B7%7D%7B2%7D%5C%5C%5C%5C)
Step 1 : simplify the equation :
![3y = 2x + 9\\\\2y = 5x + 7\\](https://tex.z-dn.net/?f=3y%20%3D%202x%20%2B%209%5C%5C%5C%5C2y%20%3D%205x%20%2B%207%5C%5C)
Step 2: Arrange the terms :
![2x - 3y = - 9\\\\5x -2 y = -7](https://tex.z-dn.net/?f=2x%20-%203y%20%3D%20-%209%5C%5C%5C%5C5x%20-2%20y%20%3D%20-7)
Step 3 : Solve for x and y :
2x - 3y = - 9 ------ ( 1 )
5x - 2y = - 7 --------- ( 2 )
_____________________
( 1 ) x 5 => 10x - 15y = - 45 ---------- (3 )
( 2) x 2 => 10x - 4y = - 14 ----------- (4 )
_______________________
( 3 ) - ( 4 ) => 0x - 11y = - 31
- 11 y = - 31
![y = \frac{31}{11}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B31%7D%7B11%7D)
Substitute y in ( 1 ) :
2x - 3y = - 9
![2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}](https://tex.z-dn.net/?f=2x%20-%203%20%28%5Cfrac%7B31%7D%7B11%7D%29%20%3D%20-%209%5C%5C%5C%5C2x%20%3D%20-9%20%2B%203%28%5Cfrac%7B31%7D%7B11%7D%29%5C%5C%5C%5C2x%20%3D%20-%209%20%2B%20%5Cfrac%7B93%7D%7B11%7D%5C%5C%5C%5C2x%20%3D%20%5Cfrac%7B-99%20%2B%2093%7D%7B11%7D%20%5C%5C%5C%5C2x%20%3D%20%5Cfrac%7B-6%7D%7B11%7D%20%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B-6%7D%7B2%20%5Ctimes%2011%7D%20%3D%20-%5Cfrac%7B3%7D%7B11%7D)
Therefore the solution to the sytem is ![( - \frac{3}{11} , \frac{31}{11})](https://tex.z-dn.net/?f=%28%20-%20%5Cfrac%7B3%7D%7B11%7D%20%2C%20%5Cfrac%7B31%7D%7B11%7D%29)
The solution of the system of equation is a point which lies
on the both the lines.
Option A : False , It says the solution lies above one of the given line.
But the solution of the system of equation always lies on
both the line.
Option B : True , says the solution is a point on the coordinate plane.
Option C : False, because if the solution is on the x-axis , then
the y coordinate in the solution would be zero.
But it is not zero.
Option D : False , the solution is the point where both the lines intersect.