2x – y = 10 ------(1) 2x – 4 = 10 2x = 10 4 = 14 x = 14/2 = 7 Hence (x , y) =( 7, 4) gives the complete solution to these two equations.In Algebra, sometimes you may come across equations of the form Ax B = Cx D where x is the variable of the equation, and A, B, C, D are coefficient values (can be both positive and negative). S (Right Hand Side) gives x = 11 Hence x = 11 is the required solution to the above equation.2x y = 15 ------(1) 3x – y = 10 ------(2) ______________ 5x = 25 (Since y and –y cancel out each other) What we are left with is a simplified equation in x alone.
Examples given next are similar to those presented above and have been shown in a way that is more understandable for kids.
If we use the method of addition in solving these two equations, we can see that what we get is a simplified equation in one variable, as shown below.
However, we can multiply a whole equation with a coefficient (say we multiply equation (2) with 2) to equate the coefficients of either of the two variables.
After multiplication, we get 2x 4y = 30 ------(2)' Next we subtract this equation (2)’ from equation (1) 2x – y = 10 2x 4y = 30 –5y = –20 y = 4 Putting this value of y into equation (1) will give us the correct value of x.
When solving a simple equation, think of the equation as a balance, with the equals sign (=) being the fulcrum or center.
Thus, if you do something to one side of the equation, you must do the same thing to the other side.
Doing the Sometimes you have to use more than one step to solve the equation.
In most cases, do the addition or subtraction step first.
Of course we have not been looking to prove this in the first place!!
Hence we conclude that there is no point in substituting the computed value into the same equation that was used for its computation. As shown in the above example, we compute the variable value from one equation and substitute it into the other.