Answer: A.

Explanation:1. Method 1: Solve the equation for y and test x-values. Given equation: $7x-4y=-84$ Isolate the term with y: $-4y = -7x - 84$ Multiply by $-1$: $4y = 7x + 84$ Divide by $4$: $y = \dfrac{7x+84}{4} = \dfrac{7}{4}x + \dfrac{84}{4} = \dfrac{7}{4}x + 21$

2. Test Table [A] using $y = \dfrac{7}{4}x + 21$: - For $x=0$: $y = \dfrac{7}{4}(0) + 21 = 0 + 21 = 21$. Table A has $y=21$. (Matches) - For $x=4$: $y = \dfrac{7}{4}(4) + 21 = 7 + 21 = 28$. Table A has $y=28$. (Matches) - For $x=8$: $y = \dfrac{7}{4}(8) + 21 = 7 \times 2 + 21 = 14 + 21 = 35$. Table A has $y=35$. (Matches) All points in Table [A] satisfy the equation.

3. Method 2: Substitute (x,y) pairs from the tables into the original equation $7x-4y=-84$. Test Table [A]: - For $(x,y) = (0,21)$: $7(0) - 4(21) = 0 - 84 = -84$. (Matches $-84$) - For $(x,y) = (4,28)$: $7(4) - 4(28) = 28 - 112 = -84$. (Matches $-84$) - For $(x,y) = (8,35)$: $7(8) - 4(35) = 56 - 140 = -84$. (Matches $-84$) Table [A] is correct.

Test Table [B]: - For $(x,y) = (0,35)$: $7(0) - 4(35) = 0 - 140 = -140$. (Does not match $-84$) Table [B] is incorrect.

(No need to test further tables if the first one matches completely, but for completeness:) Test Table [C]: - For $(x,y) = (21,0)$: $7(21) - 4(0) = 147 - 0 = 147$. (Does not match $-84$) Table [C] is incorrect.

Test Table [D]: - For $(x,y) = (21,8)$: $7(21) - 4(8) = 147 - 32 = 115$. (Does not match $-84$) Table [D] is incorrect.

Conclusion:Table [A] gives three values of x and their corresponding values of y that satisfy the equation.