Answer:
Simultaneous linear equations are a system of equations that involve two or more variables. The goal is to find the values of the variables that satisfy all the equations in the system simultaneously.
Explanation:
To solve simultaneous linear equations, there are different methods you can use. One common method is the substitution method. Here are the steps involved -
Start by choosing one of the equations and solve it for one variable in terms of the other. For example, if you have the equations:
- 2x + 3y = 7
- 4x - 5y = 1
You can choose the first equation and solve it for x:
- 2x = 7 - 3y
- x = (7 - 3y) / 2
Substitute the expression you found for x into the other equation. In this case, substitute (7 - 3y) / 2 for x in the second equation:
- 4((7 - 3y) / 2) - 5y = 1
Simplify and solve the resulting equation for y. In this case, simplify the equation:
- (28 - 12y) / 2 - 5y = 1
- 28 - 12y - 10y = 2
- 28 - 22y = 2
- -22y = 2 - 28
- -22y = -26
- y = -26 / -22
- y = 13 / 11
Substitute the value you found for y back into one of the original equations to solve for x. Using the first equation:
- 2x + 3(13 / 11) = 7
- 2x + 39 / 11 = 7
- 2x = 7 - 39 / 11
- 2x = 77 / 11 - 39 / 11
- 2x = 38 / 11
- x = 38 / 22
- x = 19 / 11
So the solution to the system of equations is x = 19/11 and y = 13/11.
Another method to solve simultaneous linear equations is the elimination method, where you eliminate one variable by adding or subtracting the equations. The steps for this method may vary depending on the specific equations given.
I hope this explanation helps you understand how to solve simultaneous linear equations. If you have any further questions, feel free to ask!