Given the system of equations:
[tex]\begin{gathered} y=2x-2 \\ y=-x+7 \end{gathered}[/tex]We will find the solution of the system by the graph
To draw each line, we need to know 2 points
So, we will substitute with 2 values of x and calculate the corresponding value of y
For the first equation: y = 2x - 2
[tex]\begin{gathered} x=0\rightarrow y=2\cdot0-2=-2 \\ x=2\rightarrow y\rightarrow=2\cdot2-2=2 \end{gathered}[/tex]So, the line passes through the points ( 0, -2 ) and ( 2, 2)
For the second line: y = -x + 7
[tex]\begin{gathered} x=0\rightarrow y=0+7=7 \\ x=2\rightarrow y=-2+7=5 \end{gathered}[/tex]so, the line passes through the points ( 0, 7) and ( 2, 5)
The graph of the system will be as shown in the following figure:
As shown in the figure:
Equation 1 is the blue line
Equation 2 is the red line
The point of intersection = ( 3, 4)
So, the answer is the solution of the system = ( 3, 4 )
