Neither x term nor y term are the same
Introduction to Neither x term nor y term are the same
- Situations observing neither x term nor y term being the same appear predominantly in simultaneous equations.
- These equations are set such that the coefficients of x and y are not equal, making it difficult to use direct addition or subtraction for a solution.
- Solving involves equating the coefficients of the x or y terms in both equations, which often requires multiplication or division.
Understanding the Principle
- The goal is to manipulate the equations such that they can be added or subtracted, resulting in the elimination of one variable.
- This requires making the coefficients of x or y in the two equations equal or opposite of each other.
- For example, in the equations 2x + 3y = 10 and 3x - 2y = 18, neither the x term nor y term have the same coefficients.
Steps to Solve
- Identify the coefficients of the x term and the y term in both equations.
- Determine a common multiple for the coefficients of either x or y, or make one’s coefficient the negative of the other.
- Modify one or both equations by multiplying or dividing to ensure the coefficients of x or y are either the same or opposite.
- Add or subtract the equations to eliminate one variable.
- Solve for the remaining variable and substitute it back into one of the original equations to find the eliminated variable’s value.
Examples
- For example, let’s consider the equations 2x + 3y = 20 and x - y = 5. These equations haven’t got similar coefficients for x or y.
- Multiply the second equation by 2, it turns into 2x - 2y = 10. Now, we can subtract these from the first equation: (2x + 3y) - (2x - 2y) = 20 - 10, giving solution 5y = 10, or y = 2. Substitute y = 2 into the original equation x - y = 5 gives x = 7.
Key Things to Remember
- Equating coefficients of variables and eliminating one variable is key in solving these kind of equations.
- It is crucial to maintain the equations’ balance when performing operations like addition, subtraction, multiplication, or division.
- Be cautious of the signs while adding or subtracting equations.