Question 4158: How do I solve an equation such as x+4y=8 or 3x-5y=16,to determine whether the given points, (0,2) and (2,2) are the solutions to the given equation? Also how would I determine the value of b so that the point given is a solution point of the equation, such as (3,0), 2x-y=b or (-5,6), 3x-2y=b?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! You can't really "solve" equations such as: x + 4y = 8 or 3x - 5y = 16 unless they are simultaneous (systems of equations) but you can certainly "evalute" them individually, given the additional information, such as possible solution points.
x + 4y = 8 for (0, 2) Substitute 0 for x and 2 for y in the equation.
0 + 4(2)= 8
8 = 8 The point (0, 2) is indeed a solution to this equation.
Similarly: 3x - 5y = 16 for (2, 2) Again, substitute 2 for x and 2 for y.
3(2) - 5(2) = 6 - 10 = -4 not = 16 So the point (2, 2) is not a solution.
The next two are evaluated in a similar manner:
2x - y = b for (3, 0) Substitute 3 for x and 0 for y.
2(3) - 0 = b
6 = b So, when b = 6, the point (3, 0) is a solution.
3x - 2y = b for (-5, 6) Substitute -5 for x and 6 for y.
3(-5) - 2(6) = b
-15 - 12 = b
- 27 = b So, when b = -27, the point (-5, 6) is a solution.
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