Given:
The system of linear equations are [tex]x+2y=4[/tex] and [tex]2x-y=3[/tex]
We need to determine the solution to the system of equations by graphing.
Graphing the equation [tex]x+2y=4[/tex]:
To graph the equation [tex]x+2y=4[/tex], let us determine the x and y intercepts.
x - intercept: When y = 0, then [tex]x+2(0)=4 \implies x=4[/tex]
y - intercept: When x = 0, then [tex]0+2y=4 \implies y=2[/tex]
The coordinates are (4,0) and (0,2)
Thus, the joining the coordinates of x and y intercept, we get the line for the equation [tex]x+2y=4[/tex]
Graphing the equation [tex]2x-y=3[/tex]:
To graph the equation [tex]2x-y=3[/tex], let us determine the x and y intercepts.
x - intercept: When y = 0, then [tex]2x-0=3 \implies x=-1.5[/tex]
y - intercept: When x = 0, then [tex]2(0)-y=3 \implies y=-3[/tex]
The coordinates are (-1.5,0) and (0,-3)
Thus, joining the coordinates of x and y intercepts, we get the line for the equation [tex]2x-y=3[/tex]
Solution:
The solution of the two equations is the point of intersection of two lines in the graph.
Let us determine the solution using substitution method.
Substituting [tex]x=4-2y[/tex] in the equation [tex]2x-y=3[/tex], we get;
[tex]2(4-2y)-y=3[/tex]
[tex]8-4y-y=3[/tex]
[tex]8-5y=3[/tex]
[tex]-5y=-5[/tex]
[tex]y=1[/tex]
Thus, the value of y is 1.
Substituting [tex]y=1[/tex] in the equation [tex]2x-y=3[/tex], we have;
[tex]2x-1=3[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
Thus, the value of x is 2.
Therefore, the solution of the system of equations is (2,1)
