State true or false.The solutions of algebraic expressions a(x+y) +b(x-y) =a2-ab+b2 and a(x+y) -b(x-y) =a2+ab+b2 would be and .

Question

State true or false.The solutions of algebraic expressions a(x+y) +b(x-y) =a2-ab+b2 and a(x+y) -b(x-y) =a2+ab+b2 would be  and .

Accepted Answer

The given statement is true.Concept- We shall use the elimination method to answer this question. We will be able to solve the problem further if we use the elimination approach to eliminate one of the terms with the variable. Because there are algebraic equations, we shall utilize elimination with caution.We will consider  and. We shall now employ the elimination process. We will delete the phrase using this way by combining equations I and (ii) . As a result, we haveAs a result,We'll use 'a' as a common term from the left side of the equation now. As a result, we have a new equation which can also be written as .Now we will eliminate the term  by subtracting the equations (i) and (ii) . Therefore we haveAs a result,We shall now consider the term 'b' to be a common term from the left side of the equation. As a result, we receive  which after solving can be written as  or we have We will use the elimination approach again on equations (iii) and (iv) to eliminate the variable y. As a result, we shall combine equations (iii) and (iv) . As a result, we receiveAs a result, we now have a new equation, which is as follows or . In this stage, we will apply substitution. That is we will substitute the value of  given as  in equation (iv) . As a result, we receiveTherefore, the value of .So, the required values of  and .Hence, the answer is option 1.

State true or false.

The solutions of algebraic expressions a(x+y) +b(x-y) =a2-ab+b2 and a(x+y) -b(x-y) =a2+ab+b2 would be and .

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