Question

substitution methods sums​

Answer 1

Answer:

Solve for ‘x’ and ‘y’:

x + y = 5.

3x + y = 11.

Solution:

x + y = 5 …………… (i)

3x + y = 11 …………… (ii)

Since we are given two different equations in terms of two different linear equations, let us try to solve them using the concept of method of substitution:

From 1st eq. we find that y = 5 - x.

Substituting value of y in eq. (ii), we get;

3x + 5 - x = 11.

⟹ 2x = 11 - 5

⟹ 2x = 6

⟹ x = 6/2

⟹ x = 3.

Substituting x = 3 in y = 5 – x, we get;

y = 5- x

⟹ y = 5 - 3

⟹ y = 2.

Hence, x = 3 and y = 2.

Explanation:

Steps involved in solving linear equations in two variables by method of substitution:

Step I: Examine the question carefully and make sure that two different linear equations are given in same two variables.

Step II: Choose any one of the equation from two given equations and try to find out value of any one variable in terms of another variable.

Step III: Now substitute the value of this variable that we found from first equation into the second equation.

Step IV: As we substitute the value of one variable into the second equation, we’ll find that the equation has been converted into a linear equation in one variable.

Step V: Earlier we have learnt concept of solving linear equation in one variable. Solve the linear equation in one variable hence formed by using the same concept.

Step VI: As we find out the value of one variable, substitute it in the equation of previous variable to find out its value.

In this way, values of variables are calculated using the concept of method of substitution.

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