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:

0.5x + 0.7y = 0.74  …… (1)

0.3x + 0.5y = 0.5  …… (2)

Step 1: Remove Decimals

Multiply both equations by 10:

5x + 7y = 7.4  …… (3)

3x + 5y = 5  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (4):

3x + 5y = 5

⇒ 5y = 5 − 3x

⇒ y = ^{5 − 3x}/₅  …… (5)

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

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

5x + 7( ^{5 − 3x}/₅ ) = 7.4

Multiply the whole equation by 5:

25x + 35 − 21x = 37

4x = 2

⇒ x = 0.5

Step 4: Find the Value of y

Substitute x = 0.5 in equation (5):

y = ^{5 − 3(0.5)}/₅

y = ^{5 − 1.5}/₅

y = ^3.5/₅

y = 0.7

Final Answer

∴ The solution of the given system of equations is:

x = 0.5 and y = 0.7

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of linear equations is (0.5, 0.7).