See below for explanation.
Step-by-step explanation:
As we know, if we substitute a solution in an equation, there can be two circumstances:
True - If both sides of equation are equal or same after substituting the solution in an equation, that equation is true and that means a point or solution lies on the graph.False - If both sides of equation are not equivalent or different after substituting the solution in an equation, that equation is false and that means a point or solution does not lie on graph.
What does substituting the solution tell you? It tells you whether if that solution you have solved or got is correct or not. Graph wise, a point is a part of an equation if LHS = RHS but a point lies differently or separates from graph if LHS ≠RHS.
KEYWORD
LHS - Left-Handed Side - It is always used to refer as left side of equation.RHS - Right-Handed Side - It is always used to refer as right side of equation.
Do you know? A single equation such as x + 5 = 2 can be written in simultaneous equations by letting both LHS and RHS = y as we obtain y = x + 5 for first equation and y = 2 as second equation.
Next, let’s talk about simultaneous equations or system of equations. They are technically the same as one-variable equation except you learn how to convert from one-variable equations to two-variable simultaneous equations and some substitutions method as well as learn some tricks to solve for simultaneous equations. The solution in two-variable simultaneous equations is in (x,y) term so you have both x and y solution. Instead of substituting one x-value solution, unlike simultaneous equations, you need to substitute both x and y.
I said that substituting the solution(s) in mathematics are to check whether if that point or solution does lie on a graph. If a point lies on a graph or equation, that solution is valid and correct - if not, the solution is incorrect.
We have cleared out the reason why we have to substitute the solution(s) in to check. Now, why do we have to substitute in both equations rather only one? The answer is to make sure in 100%. Sometimes, when substituting the (x,y) solution in simultaneous equations, one of two equations may not have same LHS and RHS respectively.
For example, when substituting x = 2 and y = 4 in first equation, we get 2 = 2 but when we substitute in the second equation, we get 4 = 2. See that the first equation is true when substituting the solution in because both sides are equal but the second equation is false because both sides are not equal. That means (2,4) is not solution to the simultaneous equations as the second equation is false. For a solution to exist in simultaneous equations, a point (x,y) must satisfy both equations which means both equations have to be true when substituting a solution (x,y).
To summarize what I said all above:-
Substituting solutions in the simultaneous equations is to check whether if the solutions are correct or apart of graphs/equations.If a one-variable equation is true i.e 3 = 3 as example when substituting a solution in then the solution is correct. Otherwise, it’s not correct.If a two-variable equations are true for both LHS and RHS i.e both equations must have same LHS and RHS respectively then the solutions are correct. Otherwise, it’s not, even if one equation has same LHS and RHS but if the second equation does not have same LHS and RHS then the solutions are false.
If you still have questions or queries about this problem or my answer, you can let me know in the comment!
