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.
The solution, no matter how complicated, is accompanied with steps which go in detail to explain the problem and it's properties.
I use this app mostly to check my work and see exactly where I went wrong in solving.
x y = 15 x 5/2 = 15 x = 15 – 5/2 x = 25/2 Hence (x , y) = (25/2, 5/2) is the solution to the given system of equations. In Elimination Method, our aim is to "eliminate" one variable by making the coefficients of that variable equal and then adding/subtracting the two equations, depending on the case.
In this example, we see that the coefficients of all the variable are same, i.e., 1.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.The joy he felt when he actually understood the problem he was looking at was amazing. Photomath is a proud winner of 4YFN competition in Barcelona, the world's largest startup competition on mobile technologies and business models.He now doesn't feel hopeless and has a sense of accomplishment. Photomath also received a Netexplo Forum Award for its work in educational technology.In solving these equations, we use a simple Algebraic technique called "Substitution Method".In this method, we evaluate one of the variable value in terms of the other variable using one of the two equations.And that value is put into the second equation to solve for the two unknown values.The solution below will make the idea of Substitution clear. x y = 15 -----(2) (10 y) y = 15 10 2y = 15 2y = 15 – 10 = 5 y = 5/2 Putting this value of y into any of the two equations will give us the value of x.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.