Question

Solve the equations using the elimination method:
5a – 6b = 2
6a – 5b = 9
(a) (4, – 3)
(b) (– 4, 3)
(c) (4, 3)
(d) (– 4, – 3)

Answer 1

Hint: Consider the given two equations and multiply the first equation by 6 and the second equation by 5 and subtract each other to solve the values of a and b for which the equation satisfies.

Complete step-by-step answer:
In this question, we are given that the two equations are 5a – 6b = 2 and 6a – 5b = 9 and we have to find the values of a and b for which the two equations satisfy. For solving the two equations, we will use the method of elimination which is done in steps.
(i) At first, find the two equations that have the same variable. Then we have to multiply each equation by a number such that their coefficients are the same.
(ii) After doing the above process, we will subtract the two newly formed equations.
(iii) We will repeat until we are left with a single variable, after that we will solve for it.
(iv) After finding the value of the solved variable, we will substitute back into the original equation to find the other value as well.
The given equation in the question are:
\[5a-6b=2....\left( i \right)\]
\[6a-5b=9.....\left( ii \right)\]
After this, first, multiply the equation (i) by 6 and equation (ii) by 5, we get,
\[30a-36b=12\]
\[30a-25b=45\]
Now, subtracting both the equations, we get,
– 11b = – 33
So, we get the value of b as 3.
Now, we will substitute the value of b in equation (i), we get,
\[5a-6\times 3=2\]
\[5a-18=2\]
\[5a=20\]
a = 4
Hence, the value of a and b is 4 and 3 respectively.
So, the correct option is (c).

Note: We can check the value of a and b are right or wrong, by substituting it in the given equations of the problem. If they satisfy, then the answers we got are right. If LHS=RHS we get only then the values obtained are the correct one else they are not correct and we need to check once again.