How can we solve the system of equations 3x + 2y = 5 and x + y = 10?

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To solve the system of equations given by 3x + 2y = 5 and x + y = 10, we can use the substitution or elimination method. Here, we’ll use the substitution method for clarity.

Step 1: Solve one of the equations for one variable

Let’s solve the second equation for y: 

x + y = 10  
=> y = 10 - x

Step 2: Substitute into the other equation

Next, we substitute y = 10 – x into the first equation:

3x + 2(10 - x) = 5

Now, expanding this gives:

3x + 20 - 2x = 5

Step 3: Simplify and solve for x

Now, combine like terms:

(3x - 2x) + 20 = 5  
=> x + 20 = 5

To isolate x, subtract 20 from both sides:

x = 5 - 20  
=> x = -15

Step 4: Substitute back to find y

Now that we have x = -15, we can find y using our earlier expression:

y = 10 - (-15)  
=> y = 10 + 15  
=> y = 25

Conclusion

We have found the solution to the system of equations:

  • x = -15
  • y = 25

Therefore, the pair (x, y) = (-15, 25) is the solution to the system of equations.

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