Given:
The given system of equations is:
To find:
The solution to this system of equations by graphing.
Solution:
We have,
The table of values for first equation is:
x y
0 1
1 -1
Plot the points (0,1) and (1,-1) on a coordinate plane and connect them a straight line.
The table of values for second equation is:
x y
0 -4
2 -3
Plot the points (0,-4) and (2,-3) on a coordinate plane and connect them a straight line.
The graphs of given equations are shown in the below figure.
From the below figure, it is clear that the lines intersect each other at point (2,-3). So, the solution of the given system of equations is (2,-3).
Therefore, the solution to this system of equations is:
x-coordinate: 2
y-coordinate: -3
The line drops 4 units between the points (1, 6) and (6, 2) as it goes over 5 units. Thus the point-slope form of the equation can be written as
... y - k = m(x - h) . . . . . . line with slope m through point (h, k)
... y - 6 = (-4/5)(x - 1)
Multiplying by 5 and subtracting the right side gives ...
... 5y - 30 = -4x +4
... 4x + 5y - 34 = 0 . . . . . equation in general form
