Given the system of equations:
[tex]\begin{gathered} y=-\frac{2}{3}x+3 \\ y=2x-5 \end{gathered}[/tex]
The equations represents the graph of the lines
To graph a line we need two points
Substitute with two value of x then find y
For the first equation:
[tex]y=-\frac{2}{3}x+3[/tex]
When x = 0 , y = 3
When x = 3 , y = 1
So, the line passing through the points ( 0 , 3 ) and ( 3 , 1 )
The following image represents the graph of the first equation:
For the second equation:
[tex]y=2x-5[/tex]
When x = 0 , y = -5
When x = 2 , y = -1
So, the line passing through the points ( 0 , -5 ) and (2 , -1)
The following image represents the line of the second equation .
Now, we will make the two lines on the same graph to find the solution of the system of equations:
As shown, the point of intersection is (3 , 1)
So, the solution of the system = ( 3 , 1 )
To check the answer, substiute with the point (3 , 1 ) at both equations:
So, for the first equation:
when x = 3
[tex]y=-\frac{2}{3}\cdot3+3=-2+3=1\text{ (true)}[/tex]
For the second equation:
when x = 3
[tex]y=2\cdot3-5=6-5=1\text{ (true)}[/tex]
