Solve the System of Linear Equations Using Cross-Multiplication Method

Video Explanation

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

Solution

Question: Solve the following system of equations using cross-multiplication method:

2x − y = 6  …… (1)

x − y = 2  …… (2)

Step 1: Write Equations in Standard Form

2x − y − 6 = 0  …… (1)

x − y − 2 = 0  …… (2)

Step 2: Compare with ax + by + c = 0

From equation (1): a₁ = 2, b₁ = −1, c₁ = −6

From equation (2): a₂ = 1, b₂ = −1, c₂ = −2

Step 3: Apply Cross-Multiplication Formula

x / (b₁c₂ − b₂c₁) = y / (a₂c₁ − a₁c₂) = 1 / (a₁b₂ − a₂b₁)

Substitute values:

x / [ (−1)(−2) − (−1)(−6) ] = y / [ 1(−6) − 2(−2) ] = 1 / [ 2(−1) − 1(−1) ]

x / (2 − 6) = y / (−6 + 4) = 1 / (−2 + 1)

x / (−4) = y / (−2) = 1 / (−1)

Step 4: Find the Values of x and y

x / (−4) = 1 / (−1)

⇒ x = 4

y / (−2) = 1 / (−1)

⇒ y = 2

Final Answer

∴ The solution of the given system of equations is:

x = 4 and y = 2

Conclusion

Thus, by using the cross-multiplication method, we find that the solution of the given system of linear equations is (4, 2).