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We are given that y = 24 – 4x ------(1) 2x y/2 = 12 ------(2) Here we choose equation (1) to compute the value of x.Since equation (1) is already in its most simplified form: (Putting this value of y into equation (2) and then solving for x gives) 2x (24-4x)/2 = 12 ------(2) (∵ y = 24 – 4x) 2x 24/2- 4x/2 = 12 2x 12 – 2x = 12 12 = 12 You might feel that this is the same scenario as discussed above (that of 24 = 24). You are trying to jump at a conclusion a bit too early.
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.
i.e., 5x = 25 (Dividing this equation throughout by 5 gives) 5x/5 = 25/5 x = 5 (Putting this value of x into equation (1) gives) 2(5) y = 15 10 y = 15 Which is another equation in a single variable y.
Let us solve the given system now We are given that 2x – 2y = –2 ------(1) x y = 24 ------(2) Now the next question is: which equation to pick up. One can simply choose an equation that makes the calculations simpler.
E.g., in this example, the equation (2) is easier to work on.
0≠ –2 Hence the two equations constitute an inconsistent system of linear equations and thus do no have a solution (At no point do the two straight lines intersect = In this method of equation solving, we work out on any of the given equations for one variable value, and then substitute that value in the other equation.
Activities To Improve Critical Thinking - How To Solve An Algebra Problem
It gives us an equation in a single variable and we can use a single variable equation solving technique to find the value of that variable (as shown in examples above).
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.
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.