What is the solution to the system of linear equations 2x + 3y = 3 and 7x + 3y = 24?

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To solve the system of linear equations:

  • Equation 1: 2x + 3y = 3
  • Equation 2: 7x + 3y = 24

We can use either the substitution method or the elimination method. Here, we’ll use the elimination method.

Step 1: Align the equations

We start with the two equations:

2x + 3y = 3   (1)
7x + 3y = 24  (2)

Step 2: Eliminate one variable

To eliminate y, we can subtract equation (1) from equation (2). Since both equations have 3y in common, we can subtract equation (1) directly:

(7x + 3y) - (2x + 3y) = 24 - 3

This simplifies to:

5x = 21

Step 3: Solve for x

Now, we solve for x:

x = 21 / 5
x = 4.2

Step 4: Substitute x back into one of the original equations

Next, we use the value of x to find y. We can substitute x = 4.2 into equation (1):

2(4.2) + 3y = 3
8.4 + 3y = 3
3y = 3 - 8.4
3y = -5.4
y = -5.4 / 3
y = -1.8

Step 5: Solution

Thus, the solution to the system of equations is:

(x, y) = (4.2, -1.8)

Conclusion

The values you found indicate that when x is 4.2 and y is -1.8, both equations are satisfied. You can verify by plugging these values back into the original equations to ensure they hold true.

This process illustrates how to solve a system of linear equations using the elimination method.

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