Answer:
2nd graph in yellow
Explanation:
The system of equations needed to solve the given equations is . Thus, the correct graph is the top-right graph. Its plotted below.
How to find the system of equations needed to solve an equation?
An equation usually consists of equality of two mathematical expressions. Let it be
�
=
�
A=B . If we take them to be equal to third variable, then:
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=
�
=
�
A=B=C type of equation is obtained.
We can then take it as system of two equations as:
�
=
�
�
=
�
A=C
B=C
Solution to this system will give us the solution to the considered equation
What is a solution to a system of equations?
For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs.
For the given case, we are given that:
2
�
−
1
=
�
+
2
2
x
−1=x+2
Taking these two mathematical expression equal to 'y', we get:
2
�
−
1
=
�
+
2
=
�
2
x
−1=x+2=y
or
�
=
2
�
−
1
�
�
�
�
=
�
+
2
y=2
x
−1
and
y=x+2
Plotting these two functions on the X-Y plane, the common point of these curves is the common value which can satisfy both the equations simultaneously, and thus, being the solution to the considered system of equations.
Thus, the solutions are those two points that are intersections of those two curves.