Question 62900
QUESTION:

Solve the equation for x and y.    x+2y=-5  x=2y-1
 
choices are:  (5,3)   (5,0)    (-3,-1)    (1,-3)

ANSWER:  

x+2y=-5 ----------------------(1) 

x=2y-1  -----------------------(2)

(5,3)
Input the values x = 5 and y = 3 in both the equations;

(1) ==> 5+ 2 *3 = 5 + 6 = -11, which is not equal to the right side (ie: -5)


 If the given point does not satisfy any one of the given equation, then it is not a solution.

Now take the second point (5,0) and substitute  in the given equations.


==> 5 + 2 * 0 = 5 which is not equiatl to -5


so (5,0) is not a solution.


Now take the third point (-3, -1)


==> -3 + 2 * -1 = -3 + -2 = -5, which is equal to the right side.

Again substitute these values in the second equation,


==> -3 = 2 * -1 - 1


==> -3 =  -2 - 1

==> -3 = -3


That is both sides of the equations  are same.


So the point (-3, -1 ) is a solution for the given equations.


We have one more point( 1, -3 ), let's check that also.

(1)==>  1+ 2 * -3 = -5

==>   1 + -6  = -5

==>   -5 = -5, that is the point satisfies the first equation.


Now check this point with the second equation.

==>  1 = 2 * -3 - 1


==>  1 = -6 - 1

==>  1 = -7, which is not correct.

so (1, -3) is not a solution.


Conclusion: 

The point (-3, -1 )  satisfies both the equation, so it the solutionm for the given pair of equation.

So solution is  x = -3 and y = -1