Math Problem Statement

Is (2, 1) a solution to this system of equations? 10x + y = 3 and 2x + 16y = 20.

Solution

To determine if the point (2,1)(2, 1) is a solution to the given system of equations:

System of equations:

  1. 10x+y=310x + y = 3
  2. 2x+16y=202x + 16y = 20

Step-by-step solution:

We substitute x=2x = 2 and y=1y = 1 into both equations:

Equation 1: 10x+y=310x + y = 3

10(2)+1=20+1=21310(2) + 1 = 20 + 1 = 21 \neq 3 This equation is not satisfied.

Equation 2: 2x+16y=202x + 16y = 20

2(2)+16(1)=4+16=202(2) + 16(1) = 4 + 16 = 20 This equation is satisfied.

Conclusion:

Since the first equation is not satisfied, the point (2,1)(2, 1) is not a solution to the system of equations. The correct answer is NO.

Would you like further details or have any questions?


Related Questions:

  1. What does it mean for a point to be a solution to a system of equations?
  2. How do you graphically verify if a point satisfies a system of equations?
  3. How can we solve a system of equations algebraically to find solutions?
  4. What are some common methods for solving systems of linear equations (e.g., substitution, elimination)?
  5. Can a system of linear equations have no solution, one solution, or infinitely many solutions?

Tip:

Always substitute the given point into all equations of the system to verify if it satisfies them. If it fails for even one equation, it is not a solution!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Systems of Equations
Substitution

Formulas

Substitution of x and y into equations
Verification: ax + by = c

Theorems

System of Linear Equations

Suitable Grade Level

Grades 7-9