Can you explain to me the cross multiplication rule for finding the value of x and y for a set of linear equations in two variables?

Question

Answer

Understanding Cross Multiplication Rule
The cross multiplication rule is a method used to solve a system of linear equations in two variables (x and y). It involves finding the values of x and y by cross multiplying the coefficients of the variables in the equations.

Steps to Apply Cross Multiplication Rule
• Step 1: Write down the given system of linear equations in the form of Ax + By = C.
• Step 2: Cross multiply the coefficients of x and y from each equation.
• Step 3: Set the two resulting equations equal to each other and solve for either x or y.
• Step 4: Substitute the value of x or y back into one of the original equations to find the other variable.

Example
Let's consider the following system of equations:
2x + 3y = 7
4x - 5y = 8

Cross Multiplying
• From the first equation: 2x * (-5) = 4x * 3
• Simplifying: -10x = 12x
• Solving for x: x = 1

Substitute and Solve
• Substitute x = 1 into the first equation: 2(1) + 3y = 7
• Simplifying: 2 + 3y = 7
• Solving for y: y = 5/3

Conclusion
Using the cross multiplication rule, we found the values of x and y for the given system of equations. This method is a useful tool for solving linear equations in two variables efficiently.

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