Math Problem Statement

Solve the system of equations: x + y = 5 and x - y = 3.

Solution

The image provided shows a mathematical problem involving systems of linear equations in two variables (in Indonesian):

The key part of the question seems to state:

  • x+y=5x + y = 5
  • xy=3x - y = 3

This is a system of linear equations that can be solved by the method of substitution, elimination, or graphing.

Let's solve it using the elimination method:

The system of equations is: 1. x+y=51. \ x + y = 5 2. xy=32. \ x - y = 3

Step 1: Add the two equations: (x+y)+(xy)=5+3(x + y) + (x - y) = 5 + 3 2x=82x = 8 x=82=4x = \frac{8}{2} = 4

Step 2: Substitute x=4x = 4 into the first equation x+y=5x + y = 5: 4+y=54 + y = 5 y=54=1y = 5 - 4 = 1

Thus, the solution is x=4x = 4 and y=1y = 1.

Would you like me to provide details on graphing the solution or further steps in solving systems of equations?

Here are 5 relative questions to expand your understanding:

  1. What are other methods to solve systems of linear equations?
  2. How can graphing help in visualizing solutions to linear systems?
  3. How do you determine if a system has no solution or infinite solutions?
  4. Can we apply matrix methods, such as Gaussian elimination, to this system?
  5. How would the solution change if one equation were modified slightly?

Tip:

When solving systems of equations, always check the possibility of dependent or inconsistent systems, where lines might overlap (infinite solutions) or be parallel (no solutions).

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

x + y = 5
x - y = 3

Theorems

Elimination Method for Systems of Equations
Substitution Method

Suitable Grade Level

Grades 7-9