If (0, a) and (b, 0) are the solutions of the linear equation 3x = 7y – 21. Find a and b.
The Correct Answer and Explanation is:
To solve for aaa and bbb, we need to substitute the given points into the equation and solve for the unknowns.
The equation given is: 3x=7y−213x = 7y – 213x=7y−21
Step 1: Substituting the point (0, a)
Substitute x=0x = 0x=0 and y=ay = ay=a into the equation: 3(0)=7(a)−213(0) = 7(a) – 213(0)=7(a)−21
This simplifies to: 0=7a−210 = 7a – 210=7a−21
Now, solve for aaa: 7a=21⇒a=217=37a = 21 \quad \Rightarrow \quad a = \frac{21}{7} = 37a=21⇒a=721=3
So, a=3a = 3a=3.
Step 2: Substituting the point (b, 0)
Next, substitute x=bx = bx=b and y=0y = 0y=0 into the equation: 3(b)=7(0)−213(b) = 7(0) – 213(b)=7(0)−21
This simplifies to: 3b=−213b = -213b=−21
Now, solve for bbb: b=−213=−7b = \frac{-21}{3} = -7b=3−21=−7
So, b=−7b = -7b=−7.
Conclusion:
The values of aaa and bbb are:
- a=3a = 3a=3
- b=−7b = -7b=−7
Thus, the solutions to the equation are a=3a = 3a=3 and b=−7b = -7b=−7.
