Question

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

Answer 1

Answer:

option B

Step-by-step explanation:

Given :

$y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}$

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

                                        $y = \frac{31}{11}$

              Substitute y in ( 1 ) :

                     2x - 3y = - 9

                     $2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}$

Therefore the solution to the sytem is $( - \frac{3}{11} , \frac{31}{11})$

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.