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:

15/u + 2/v = 17  …… (1)

1/u + 1/v = ³⁶/₅  …… (2)

Step 1: Substitute 1/u = x and 1/v = y

Let 1/u = x and 1/v = y

Then equations (1) and (2) become:

15x + 2y = 17  …… (3)

x + y = ³⁶/₅  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (4):

y = ³⁶/₅ − x  …… (5)

Step 3: Substitute the Value of y in Equation (3)

Substitute y from equation (5) into equation (3):

15x + 2( ³⁶/₅ − x ) = 17

15x + ⁷²/₅ − 2x = 17

13x + ⁷²/₅ = 17

Convert 17 into fraction:

13x + ⁷²/₅ = ⁸⁵/₅

⇒ 13x = ¹³/₅

⇒ x = ¹/₅

Step 4: Find the Value of y

Substitute x = ¹/₅ in equation (5):

y = ³⁶/₅ − ¹/₅

y = ³⁵/₅

y = 7

Step 5: Find the Values of u and v

Since x = 1/u,

1/u = ¹/₅ ⇒ u = 5

Since y = 1/v,

1/v = 7 ⇒ v = ¹/₇

Final Answer

∴ The solution of the given system of equations is:

u = 5 and v = ¹/₇

Conclusion

Thus, by substituting 1/u = x and 1/v = y and using the substitution method, we find that the solution of the given system of equations is (u, v) = (5, 1/7).