The solution of the equation is [tex]x=3[/tex] and [tex]y=1[/tex]
Explanation:
The equations are [tex]y=x-2[/tex] and [tex]y=-2 x+7[/tex]
First we shall solve the equation graphically.
The image of the graph is attached below.
This contains the solution to the system of equations.
The equations [tex]y=x-2[/tex] and [tex]y=-2 x+7[/tex] are plotted on the graph.
The intersection of these two equations are the solutions of the system of equations.
Thus, the intersection of the two equations are [tex]x=3[/tex] and [tex]y=1[/tex]
Now, we shall solve the equation algebraically.
Let us solve the equation using substitution method.
Let us substitute [tex]y=x-2[/tex] in [tex]y=-2 x+7[/tex], we get,
[tex]x-2=-2x+7[/tex]
Adding both sides by 2x, we have,
[tex]3x-2=7[/tex]
Adding both sides by 2, we get,
[tex]3x=9[/tex]
Dividing both sides by 3,
[tex]x=3[/tex]
Thus, the value of x is 3.
Substituting [tex]x=3[/tex] in [tex]y=x-2[/tex], we get,
[tex]y=3-2\\y=1[/tex]
Thus, the value of y is 1.
Hence, The solution of the equation is [tex]x=3[/tex] and [tex]y=1[/tex]
