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:

x + 2y + 1 = 0  …… (1)

2x − 3y − 12 = 0  …… (2)

Step 1: Write the Equations in Standard Form

x + 2y = −1  …… (1)

2x − 3y = 12  …… (2)

Step 2: Compare with Standard Form

ax + by + c = 0

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

From equation (2): a₂ = 2, b₂ = −3, c₂ = −12

Step 3: Apply Cross-Multiplication Formula

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

Substitute values:

x / [2(−12) − (−3)(1)] = y / [2(1) − 1(−12)] = 1 / [1(−3) − 2(2)]

x / (−24 + 3) = y / (2 + 12) = 1 / (−3 − 4)

x / (−21) = y / 14 = 1 / (−7)

Step 4: Find the Values of x and y

x / (−21) = 1 / (−7)

⇒ x = 3

y / 14 = 1 / (−7)

⇒ y = −2

Final Answer

∴ The solution of the given system of equations is:

x = 3 and y = −2

Conclusion

Thus, by using the cross-multiplication method, we find that the solution of the given system of linear equations is (3, −2).