How can I solve the linear equations 2x + y = 5 and 3x + 2y = 4?

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Solving the Linear Equations

We have the following system of linear equations:

  • Equation 1: 2x + y = 5
  • Equation 2: 3x + 2y = 4

Step 1: Solve Equation 1 for y

From Equation 1, we can express y in terms of x:

y = 5 - 2x

Step 2: Substitute for y in Equation 2

Now, we substitute this expression for y into Equation 2:

3x + 2(5 - 2x) = 4

Expanding this gives:

3x + 10 - 4x = 4

Simplifying further:

-x + 10 = 4

Step 3: Solve for x

Now, we isolate x:

-x = 4 - 10
-x = -6
x = 6

Step 4: Substitute x back to find y

Next, we substitute x back into the equation for y:

y = 5 - 2(6)

Calculating this gives:

y = 5 - 12
y = -7

Final Solution

Thus, the solution to the system of equations is:

  • x = 6
  • y = -7

Conclusion

We have successfully solved the system of linear equations. The values for x and y satisfy both equations, confirming the solution is correct.

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