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1. Simultaneous Linear Equations and Inequalities Quiz
2. 10 MCQS on Solving Simultaneous Inequalities
3. Best 10 MCQS on Solving simultaneous equations graphically
4. Best 10 MCQS on Solving problems involving simultaneous equations
5. 10 MCQS on equation in two variables
Solving Simultaneous Equations consists of finding the values of x and y such that both equations or equalities are verified. For example, x-y=0 and x+y=2 is a simultaneous equations. It is clear that x=1 and y=1 is the solution for this simultaneous equations. But how can we obtain these values. We have 5 methods: substitution, elimination, comparison, the Cramer’s rule and graphical method.
1. Substitution method
In this method, we choose one equation and find the subject of one variable in terms of another variable. Then we replace this variable in another equation. After, we get the equation of one variable which we solve and get the value of one variable. This value is replaced in the other equation to get the value of another variable.
For our example above, we first of all number the equations: x-y=0 (1) and x+y=2 (2). Now from the equation (1) x=y (3). Then, we replace this equatioin (3) into the equation (2) to get y+y=2 (4). Then, the equatioin (4) gives us 2y=2 and therefore y=1. From the equation (3), we obtain finally x=1.
2. Elimination method
Here, we choose a variable that we want to eliminate and multiply each equation with the numbers such that one variable can be eliminated. From the above examples, we add side by side the equations to eliminate y. Then we get 2x=2, which gives us x=1 and y=1.
3. Comparison method
In this method, we choose one variable that we want to make subject of another one. If we choose x, then we find the expression of x in terms of y in each equation. Then we equalize those two expressions of x. That is, we obtain the equation of one variable y. We solve for y and then after we replace in equation that we want to obtain the value of x.
For the above example, x=y in equation (1) and x=2-y in equation (2). The two expressions are equal to give use y=2-y. By solving, we get y=1. And we replace in one of the expressions to get the value of x.
4. Cramer’s rule method
For this method you can check here
5. Graphical Mehod
This method proves that two lines are not parallel if they intersect. That is, we draw the two lines and then read the coordinates of the interection. This intercection is a point (x,y) for which each line passes through.