Given that 3x + 5y = 17 and 2x + 3y = 11, what is the value of x + y ?

To find the value of x + y, we can use the method of substitution or elimination. Here, I'll use the elimination method.

Step 1: Multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same in both equations. This gives us:

6x + 10y = 34 6x + 9y = 33

Step 2: Subtract the second equation from the first to eliminate y:

6x + 10y - (6x + 9y) = 34 - 33 y = 1

Step 3: Substitute y = 1 into the first equation:

3x + 5(1) = 17 3x + 5 = 17 3x = 12 x = 4

So, x = 4 and y = 1. Therefore, x + y = 4 + 1 = 5.

To find the value of x + y, we can use the method of substitution or elimination. Here, I'll use the elimination method.

Step 1: Multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same in both equations. This gives us:

6x + 10y = 34 6x + 9y = 33

Step 2: Subtract the second equation from the first to eliminate x:

6x + 10y - (6x + 9y) = 34 - 33 y = 1

Step 3: Substitute y = 1 into the first equation:

3x + 5(1) = 17 3x + 5 = 17 3x = 12 x = 4

So, x + y = 4 + 1 = 5.