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:

√2x − √3y = 0  …… (1)

√3x − √8y = 0  …… (2)

Step 1: Express One Variable in Terms of the Other

From equation (1):

√2x = √3y

⇒ x = ^√3/_√2 y  …… (3)

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

Substitute x from equation (3) into equation (2):

√3 ( ^√3/_√2 y ) − √8y = 0

⇒ ³/_√2 y − √8y = 0

Step 3: Simplify the Equation

Write √8 as 2√2:

³/_√2 y − 2√2 y = 0

Take y common:

y ( ³/_√2 − 2√2 ) = 0

Convert 2√2 to fraction form:

2√2 = ⁴/_√2

So,

y ( ^{3 − 4}/_√2 ) = 0

y ( −1/√2 ) = 0

⇒ y = 0

Step 4: Find the Value of x

Substitute y = 0 in equation (3):

x = ^√3/_√2 × 0

x = 0

Final Answer

∴ The solution of the given system of equations is:

x = 0 and y = 0

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of equations is (0, 0).