situation-I: 2x + 3y=1400 situation-II: 3x + 5y=2

To solve the system of equations given by Situation I and Situation II, we can use the method of substitution or elimination. Here, we will use the elimination method for clarity.

Equations Overview

The equations are:

• Situation I: 2x + 3y = 1400
• Situation II: 3x + 5y = 2150

Step 1: Align the Equations

We want to eliminate one of the variables. To do this, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients of x the same:

• 3(2x + 3y) = 3(1400) → 6x + 9y = 4200
• 2(3x + 5y) = 2(2150) → 6x + 10y = 4300

Step 2: Subtract the Equations

Now, we subtract the first modified equation from the second:

(6x + 10y) - (6x + 9y) = 4300 - 4200

This simplifies to:

y = 100

Step 3: Substitute Back to Find x

Now that we have y, we can substitute it back into one of the original equations to find x. Using Situation I:

2x + 3(100) = 1400

2x + 300 = 1400

2x = 1100

x = 550

Final Solution

The solution to the system of equations is:

• x: 550
• y: 100

Thus, the values of x and y that satisfy both equations are 550 and 100, respectively.