SOLUTION: Is the point (5,3) a solution to this nonlinear system? 1. x²

SOLUTION: Is the point (5,3) a solution to this nonlinear system? 1. x² - 3y = 34 2x + y = 7

Question 1182581: Is the point (5,3) a solution to this nonlinear system?
1. x² - 3y = 34
2x + y = 7
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Make the substitutions, evaluate, and find out.
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

The point (5,3) means x = 5 and y = 3 pair up together.

Replace x and y with 5 and 3 in that order for each equation.

We'll start with the first equation
x^2-3y = 34
5^2-3(3) = 34
25-9 = 34
16 = 34
We get a false statement at the end, so the given point is not a solution to the system.
Both equations must be true at the same time in order to get a solution.

For the sake of completeness, I'll show the other equation as well
2x+y = 7
2(5)+3 = 7
10+3 = 7
13 = 7
This is false as well. Even if it was true, the first equation being false is sufficient to conclude that the point isn't a solution.

Answer: No, it's not a solution.

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