Solve 2x + 2y + 50 = 2x + 2y + 50 for x: Problem Solving with 2D Matrices

In summary, the conversation involves a problem in which the age of a person and their spouse must be determined using 2D matrices. The problem is not solvable due to insufficient information and the person plans to ask the teacher for clarification.
  • #1
vepore2
4
0
I just started taking geometry and discrete math and we're just learning 2d matrices. Here is a problem I can't figure out:

1) My wife and I are 6 years apart in age. If you double the sum of our ages and add 50, you get the same number as when you add 25 to the sum of our ages and double it. How old am I?

Ok so let x - be the age of him, and y be his wifes age
We can assume that he is older then his wife so

x - y = 6
Then 2(x + y) + 50 = 2(x + y + 25)

Here's is where I'm confused
Can someone tell me the next few steps into setting up this problem.
 
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  • #2
I would suggest checking that is exactly what the question states - there clearly isn't enough information there to solve. Ask the instructor if they've made a mistake.
 
  • #3
Originally posted by vepore2
x - y = 6
Then 2(x + y) + 50 = 2(x + y + 25)
This is how I understand it as well. But the second equation is trivial, so you do not have enough information.
 
  • #4
Thanks I'll ask the teacher tomorow.
 

1. How do I solve this equation using matrices?

To solve this equation using matrices, you can rewrite it in matrix form by grouping the x and y terms on one side and the constants on the other side. This will result in a matrix equation of the form Ax = b, where A is a coefficient matrix, x is a variable matrix, and b is a constant vector. Then, you can use matrix operations such as row reduction or inverse matrix to solve for x.

2. Why do we use matrices to solve equations?

Matrices provide a convenient and efficient way to represent systems of equations. By using matrix operations, we can easily manipulate and solve these equations without having to solve each individual equation separately. This is especially useful when dealing with large systems of equations.

3. Can I use different methods to solve this equation?

Yes, there are various methods that can be used to solve matrix equations, such as Gaussian elimination, Cramer's rule, and inverse matrix. The choice of method may depend on the size and complexity of the matrix and personal preference.

4. Is it possible to have multiple solutions for this equation?

It is possible to have multiple solutions for this equation if the coefficient matrix is not invertible. In this case, the system of equations is either inconsistent (has no solution) or has infinitely many solutions.

5. Can I use matrices to solve any type of equation?

Matrices can be used to solve linear equations, which have variables raised to the first power. They cannot be used to solve equations with variables raised to higher powers, such as quadratic or cubic equations. However, matrices can still be used to solve systems of nonlinear equations by using iterative methods.

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