Question

3x - y = 2 ; 2x - y =3 graph method​

Answer 1

Answer:

I can clearly not create a graph right away in matter of seconds and tell you the answer , but the only thing you need to understand is that

• both of these equations are linear, hence they represent a straight line therefore if you draw graph of both lines you'll get two lines for each equation .
• A pair of values of x and y satisfying each of the equations in the given system of two simultaneous equations(don't be scared of this simultaneous word , it just means that you have to find (x,y) such that it satisfies both equations) in x and y is called a solution of the system.
• A pair of linear equations will have either (a) a unique solution or (b) infinitely many solutions or (c) no solution.
• Now imagine if you've find solution for the system of equations or these two equations , then that means this pair of X and Y will satisfy both of the equations because it's THE solution for both of the equations, graphically that means a solution of a system of equations is just the point of intersection of lines represented by the equations in the question.

Consider the cases when you'll be drawing the graph of these equations :-

(i) If the lines intersect at a point, the pair of equations is consistent.The point of intersection gives the unique solution of the equations (which in this case is your answer).

(i) If the lines intersect at a point, the pair of equations is consistent.The point of intersection gives the unique solution of the equations (which in this case is your answer).(ii) If the lines coincide, then there are infinitely many solutions. The pair of equations is consistent. Each point on the line will be a solution(in this case , you can't write just one solution so you'll just end up answering, "many solutions exist")

(i) If the lines intersect at a point, the pair of equations is consistent.The point of intersection gives the unique solution of the equations (which in this case is your answer).(ii) If the lines coincide, then there are infinitely many solutions. The pair of equations is consistent. Each point on the line will be a solution(in this case , you can't write just one solution so you'll just end up answering, "many solutions exist")(iii) If the lines are parallel, the pair of the linear equations has no solution. The pair of linear equations is inconsistent. (because the lines will never intersect hence no point of intersection and that means no solution for system of equations).