s (-2, -7) the solution to the following system? Justify your response. 7y - 4x = 29 x = y - 5

Question

IS (-2,-7) THE SOULTION FOR THE FOLLOWING SYSTEM? JUSTIFY YOUR ANSWER.

7Y-4X=29

X=Y-5

Answer 1

If s(-2,-7) is the solution to the equations then putting x=-2 and y=-7 in them should satisfy them; but it doesn't!
Take the second equation: x=y-5. When y=-7, x would be -12, but x should be -2.
x=y-5 so 4x=4y-20. We can substitute for 4x in the other equation: 7y-4y+20=29, so 3y=9 and y=3, making x=-2.
Now both equations are satisfied.
Graphically, the two eqns can be represented by two intersecting straight lines. The point s is where they intersect, (-2,3), not (-2,-7).

Answer 2

BY SUB'S THE EQUATION                                                                                                          X=Y-5    IN                                                                                                                                             7Y-4X=29                                                                                                                                         WE GET                                                                                                                                                7Y-4Y+20=29                                                                                                                                  3Y=9                                                                                                                                                   Y=3                                                                                                                                                  SUB'S THE VALUE OF Y IN THE EQUATION                                                                             X=Y-5                                                                                                                                             X=3-5=-2                                                                                                                           THEREFORE (X,Y)=(-2,3)                                                                                                              BUT NOT (-2,-7)