Among the following given below, what are the 3 values of x and y which satisfy the given equation 5x + 3y = 30.
Among the following given below, what are the 3 values of x and y which satisfy the given equation 5x + 3y = 30.
The correct option is D (3,5), (0,10), (6,0).
Given equation: 5x + 3y = 30.
Case(1)
Value of (x,y) = (3,5), (0,10), (6,0).
Check for (3, 5)
Put x = 3 and y = 5 in equation 5x + 3y = 30.
5(3) + 3(5) = 30
5×3 + 3×5 = 30
15 + 15 = 30
30 = 30
True statement.
⇒ (3,5) is a solution of 5x + 3y = 30.
Check for (0, 10)
Put x = 0 and y = 10 in equation 5x + 3y = 30.
5(0) +3(10) = 30
5×0 + 3×10 = 30
0 + 30 = 30
30 = 30
True statement.
⇒ (0,10) is a solution of 5x + 3y = 30.
Check for (6, 0)
Put x = 6 and y = 0 in equation 5x + 3y = 30.
5(6) + 3(0) = 30
5×6 + 3×0 = 30
30 + 0 = 30
30 = 30
True statement.
⇒ (6,0) is a solution of 5x + 3y = 30.
Case(2)
Value of (x,y) = (2,1), (1,2), (2,3).
Check for (2, 1)
Put x = 2 and y = 1 in equation 5x + 3y = 30.
5(2) + 3(1) = 30
5×2 + 3×1 = 30
10 + 3 = 30
13 = 30
False statement.
Check for (1, 2)
Put x = 1 and y = 2 in equation 5x + 3y = 30.
5(1) + 3(2) = 30
5×1 + 3×2 = 30
5 + 6 = 30
11 = 30
False statement.
Check for (2, 3)
Put x = 2 and y = 3 in equation 5x + 3y = 30.
5(2) + 3(3) = 30
5×2 + 3×3 = 30
10 + 9 = 30
19 = 30
False statement.
Case(3)
Value of (x,y) = (3,1), (4,2), (2,4).
Check for (3, 1)
Put x = 3 and y = 1 in equation 5x + 3y = 30.
5(3) + 3(1) = 30
5×3 + 3×1 = 30
15 + 3 = 30
18 = 30
False statement.
Check for (4, 2)
Put x = 4 and y = 2 in equation 5x + 3y = 30.
5(4) + 3(2) = 30
5×4 + 3×2 = 30
20 + 6 = 30
26 = 30
False statement.
Check for (2, 4)
Put x = 2 and y = 4 in equation 5x + 3y = 30.
5(2) + 3(4) = 30
5×2 + 3×4 = 30
10 + 12 = 30
22 = 30
False statement.
Case(4)
Value of (x,y) = (2,0), (3,0), (1,4).
Check for (2, 0)
Put x = 2 and y = 0 in equation 5x + 3y = 30.
5(2) + 3(0) = 30
5×2 + 3×0 = 30
10 + 0 = 30
10 = 30
False statement.
Check for (3, 0)
Put x = 3 and y = 0 in equation 5x + 3y = 30.
5(3) + 3(0) = 30
5×3 + 3×0 = 30
15 + 0 = 30
15 = 30
False statement.
Check for (2, 4)
Put x = 2 and y = 4 in equation 5x + 3y = 30.
5(2) + 3(4) = 30
5×2 + 3×4 = 30
10 + 12 = 30
22 = 30
False statement.
So value of x and y are (3,5), (0,10), (6,0).
Given equation: 5x + 3y = 30.
Case(1)
Value of (x,y) = (3,5), (0,10), (6,0).
Check for (3, 5)
Put x = 3 and y = 5 in equation 5x + 3y = 30.
5(3) + 3(5) = 30
5×3 + 3×5 = 30
15 + 15 = 30
30 = 30
True statement.
⇒ (3,5) is a solution of 5x + 3y = 30.
Check for (0, 10)
Put x = 0 and y = 10 in equation 5x + 3y = 30.
5(0) +3(10) = 30
5×0 + 3×10 = 30
0 + 30 = 30
30 = 30
True statement.
⇒ (0,10) is a solution of 5x + 3y = 30.
Check for (6, 0)
Put x = 6 and y = 0 in equation 5x + 3y = 30.
5(6) + 3(0) = 30
5×6 + 3×0 = 30
30 + 0 = 30
30 = 30
True statement.
⇒ (6,0) is a solution of 5x + 3y = 30.
Case(2)
Value of (x,y) = (2,1), (1,2), (2,3).
Check for (2, 1)
Put x = 2 and y = 1 in equation 5x + 3y = 30.
5(2) + 3(1) = 30
5×2 + 3×1 = 30
10 + 3 = 30
13 = 30
False statement.
Check for (1, 2)
Put x = 1 and y = 2 in equation 5x + 3y = 30.
5(1) + 3(2) = 30
5×1 + 3×2 = 30
5 + 6 = 30
11 = 30
False statement.
Check for (2, 3)
Put x = 2 and y = 3 in equation 5x + 3y = 30.
5(2) + 3(3) = 30
5×2 + 3×3 = 30
10 + 9 = 30
19 = 30
False statement.
Case(3)
Value of (x,y) = (3,1), (4,2), (2,4).
Check for (3, 1)
Put x = 3 and y = 1 in equation 5x + 3y = 30.
5(3) + 3(1) = 30
5×3 + 3×1 = 30
15 + 3 = 30
18 = 30
False statement.
Check for (4, 2)
Put x = 4 and y = 2 in equation 5x + 3y = 30.
5(4) + 3(2) = 30
5×4 + 3×2 = 30
20 + 6 = 30
26 = 30
False statement.
Check for (2, 4)
Put x = 2 and y = 4 in equation 5x + 3y = 30.
5(2) + 3(4) = 30
5×2 + 3×4 = 30
10 + 12 = 30
22 = 30
False statement.
Case(4)
Value of (x,y) = (2,0), (3,0), (1,4).
Check for (2, 0)
Put x = 2 and y = 0 in equation 5x + 3y = 30.
5(2) + 3(0) = 30
5×2 + 3×0 = 30
10 + 0 = 30
10 = 30
False statement.
Check for (3, 0)
Put x = 3 and y = 0 in equation 5x + 3y = 30.
5(3) + 3(0) = 30
5×3 + 3×0 = 30
15 + 0 = 30
15 = 30
False statement.
Check for (2, 4)
Put x = 2 and y = 4 in equation 5x + 3y = 30.
5(2) + 3(4) = 30
5×2 + 3×4 = 30
10 + 12 = 30
22 = 30
False statement.
So value of x and y are (3,5), (0,10), (6,0).
