Solve the System of Linear Equations Using Substitution Method

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Solve the following system of equations using substitution method:

3x − (y + 7)/11 + 2 = 10  …… (1)

2y + (x + 11)/7 = 10  …… (2)

Step 1: Simplify Both Equations

From equation (1):

3x − (y + 7)/11 = 8

Multiply both sides by 11:

33x − (y + 7) = 88

33x − y − 7 = 88

33x − y = 95  …… (3)

From equation (2):

(x + 11)/7 = 10 − 2y

Multiply both sides by 7:

x + 11 = 70 − 14y

x = 59 − 14y  …… (4)

Step 2: Substitute the Value of x in Equation (3)

Substitute x from equation (4) into equation (3):

33(59 − 14y) − y = 95

1947 − 462y − y = 95

1947 − 463y = 95

463y = 1852

⇒ y = 4

Step 3: Find the Value of x

Substitute y = 4 in equation (4):

x = 59 − 14(4)

x = 59 − 56

x = 3

Final Answer

∴ The solution of the given system of equations is:

x = 3 and y = 4

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of equations is (3, 4).