Question

Is (4,-3) a solution to this system? 3x-3y=21 5x+4y=24

Answer 1

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We have the following system of linear equations:

3x-3y=21

5x+4y=24

We could solve this system through elimination: Multiply the first equation by 5 and the second equation by -3. When you add together the results, x will drop out. This is a great approach.

But you could take a short cut by subst. the coordinates (4,-3) into both of the given linear equations. IF both equations are true after this substitution, then you know that (4,-3) is a solution. Let's try it:

3(4) - 3(-3) = 21 => 12 + 9 = 21. This is true. But we must ALSO check whether (4,-3) satisfies 5x+4y=24: 5(4) + 4(-3) = 24 => 20 - 12 = 12. This is NOT equal to 24, so we must conclude that (4,-3) is NOT a solution of this system of linear equations.

Answer 2

No it is not. although it fits the first equation, it doesn’t fit the second.