Solve the following system of equations: x + 2 = 7 7x + 3x^2 = 9
Understand the Problem
The question asks to solve the system of equations for x. We can solve the first equation for x, and then substitute x into the second equation, then solve the value of $x$.
Answer
No solution.
Answer for screen readers
No solution.
Steps to Solve
-
Solve the first equation for $x$ We have the equation $x + 2 = 7$. Subtracting 2 from both sides, we get: $x = 7 - 2$ $x = 5$
-
Substitute the value of $x$ into the second equation The second equation is $7x + 3x^2 = 9$. Substituting $x = 5$, we get: $7(5) + 3(5)^2 = 9$
-
Simplify the left side of the equation $35 + 3(25) = 9$ $35 + 75 = 9$ $110 = 9$
-
Check for consistency Since $110 \neq 9$, the second equation is not satisfied when $x = 5$. Therefore, there is no solution for this system of equations.
No solution.
More Information
The system of equations has no solution because the value of $x$ obtained from the first equation does not satisfy the second equation.
Tips
A common mistake is to assume there is a solution without verifying that the value obtained from one equation satisfies the other equation in the system.
AI-generated content may contain errors. Please verify critical information
