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 = 35  …… (1)

3x + 4y = 65  …… (2)

Step 1: Write Equations in Standard Form

2x + y − 35 = 0  …… (1)

3x + 4y − 65 = 0  …… (2)

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

From equation (1): a₁ = 2, b₁ = 1, c₁ = −35

From equation (2): a₂ = 3, b₂ = 4, c₂ = −65

Step 3: Apply Cross-Multiplication Formula

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

Substitute values:

x / [1(−65) − 4(−35)] = y / [3(−35) − 2(−65)] = 1 / [2(4) − 3(1)]

x / (−65 + 140) = y / (−105 + 130) = 1 / (8 − 3)

x / 75 = y / 25 = 1 / 5

Step 4: Find the Values of x and y

x / 75 = 1 / 5

⇒ x = 15

y / 25 = 1 / 5

⇒ y = 5

Final Answer

∴ The solution of the given system of equations is:

x = 15 and y = 5

Conclusion

Thus, by using the cross-multiplication method, we find that the solution of the given system of linear equations is (15, 5).