# If a - b = 4 and a + b = 6, then find ab.

$

{\text{A}}{\text{. 5}} \\

{\text{B}}{\text{. 2}} \\

{\text{C}}{\text{. 45}} \\

{\text{D}}{\text{. 3}} \\

$

Answer

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Hint- Here, we will be using elimination method to solve the given two equations in two variables.

Given equations are $a - b = 4{\text{ }} \to {\text{(1)}}$ and $a + b = 6{\text{ }} \to {\text{(2)}}$

The above two given equations have two variables $a$ and $b$.

Adding both the equations (1) and (2), we get

$a - b + a + b = 4 + 6 \Rightarrow 2a = 10 \Rightarrow a = 5$

Put the value of $a$ in equation (1), we get

$5 - b = 4 \Rightarrow b = 5 - 4 \Rightarrow b = 1$

So, the values of the two variables that satisfy the two given equations are $a = 5$ and $b = 1$.

Hence, $ab = 5 \times 1 = 5$

Therefore, the value of $ab$ is 5.

i.e., option A is correct.

Note- These types of problems of two equations in two variables can be solved easily using substitution method or elimination method. In the substitution method, we represent one variable in terms of another variable using one equation and substitute this value in the other equation in order to get the values of both variables.

Given equations are $a - b = 4{\text{ }} \to {\text{(1)}}$ and $a + b = 6{\text{ }} \to {\text{(2)}}$

The above two given equations have two variables $a$ and $b$.

Adding both the equations (1) and (2), we get

$a - b + a + b = 4 + 6 \Rightarrow 2a = 10 \Rightarrow a = 5$

Put the value of $a$ in equation (1), we get

$5 - b = 4 \Rightarrow b = 5 - 4 \Rightarrow b = 1$

So, the values of the two variables that satisfy the two given equations are $a = 5$ and $b = 1$.

Hence, $ab = 5 \times 1 = 5$

Therefore, the value of $ab$ is 5.

i.e., option A is correct.

Note- These types of problems of two equations in two variables can be solved easily using substitution method or elimination method. In the substitution method, we represent one variable in terms of another variable using one equation and substitute this value in the other equation in order to get the values of both variables.

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