Question

Please I have my final now can someone help me with this fast

Answer 1

option B

Explanation:

Given :

`y = (2)/(3)x + 3\\\\y = (5)/(2)x + (7)/(2)\\\\`

Step 1 : simplify the equation :

`3y = 2x + 9\\\\2y = 5x + 7\\`

Step 2: Arrange the terms :

`2x - 3y = - 9\\\\5x -2 y = -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 = (31)/(11)`

Substitute y in ( 1 ) :

2x - 3y = - 9

`2x - 3 ((31)/(11)) = - 9\\\\2x = -9 + 3((31)/(11))\\\\2x = - 9 + (93)/(11)\\\\2x = (-99 + 93)/(11) \\\\2x = (-6)/(11) \\\\x = (-6)/(2 * 11) = -(3)/(11)`

Therefore the solution to the sytem is
`( - (3)/(11) , (31)/(11))`

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.