Answer:
The solution is (-1, 3).
Step-by-step explanation:
Given:
The system of equations are given as:
[tex]y=-x+2\\y=3x+6[/tex]
The slope-intercept form of a line is given as:
[tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
For the first equation [tex]y=-x+2[/tex]
[tex]m=-1,b=2[/tex]
So, the slope is negative and the change of y with x is always equal to 1.
This means that if 'x' changes from 0 to 1, then 'y' will decrease by 1 unit.
Also, the y-intercept is at (0, 2)
Now, marking the point (0, 2) on the graph and then increasing 'x' by 1 unit and decreasing 'y' by 1 unit, we get another point at (1, 1). Then draw a line a passing through these two points. The line is the graph of the first equation.
Similarly, consider the second equation.
[tex]y=3x+6[/tex]
Here,[tex]m=3,b=6[/tex]
So, we mark the point (0, 6) and then increase 'x' by 1 unit and increase 'y' by 3 units to get the point (1, 9). Draw a line passing through these 2 points.
The graphs are shown below. The point of intersection of both the lines is the required solution. As we can see from the graph, the point of intersection is at (-1. 3).
Therefore, the solution is (-1, 3).
