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:

3x + 2y + 25 = 0  …… (1)

2x + y + 10 = 0  …… (2)

Step 1: Write the Equations in Standard Form

3x + 2y = −25  …… (1)

2x + y = −10  …… (2)

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

From equation (1): a₁ = 3, b₁ = 2, c₁ = 25

From equation (2): a₂ = 2, b₂ = 1, c₂ = 10

Step 3: Apply Cross-Multiplication Formula

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

Substitute values:

x / [2(10) − 1(25)] = y / [2(25) − 3(10)] = 1 / [3(1) − 2(2)]

x / (20 − 25) = y / (50 − 30) = 1 / (3 − 4)

x / (−5) = y / 20 = 1 / (−1)

Step 4: Find the Values of x and y

x / (−5) = 1 / (−1)

⇒ x = 5

y / 20 = 1 / (−1)

⇒ y = −20

Final Answer

∴ The solution of the given system of equations is:

x = 5 and y = −20

Conclusion

Thus, by using the cross-multiplication method, we find that the solution of the given system of linear equations is (5, −20).