5x-3y=2 and 10x-6y=4 solve the following system of equations by graphing
To solve the system of equations by graphing, we can first rewrite both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
For the first equation, 5x - 3y = 2:
-3y = -5x + 2
y = (5/3)x - (2/3)
For the second equation, 10x - 6y = 4:
-6y = -10x + 4
y = (10/6)x - (4/6)
y = (5/3)x - (2/3)
Now, we can graph both equations on the coordinate plane to find their intersection point, which is the solution to the system.
Graph of y = (5/3)x - (2/3):
- Start by plotting the y-intercept at b = -2/3, which is (0, -2/3).
- Use the slope m = 5/3 to find additional points. For example, from the y-intercept:
- Move 3 units right (3/3 = 1), and 5 units up.
- The corresponding point is (3, 3/3 + (-2/3)) = (3, 1/3).
- Draw a line passing through both points.
Graph of y = (5/3)x - (2/3):
Graph of y = (5/3)x - (2/3)-+-+-+-+-+-+----+-+-+-+-+-+-+-+--+--+--+- +
| +- -+-+- - +- - +- -+ |
3 +
| * |
2 + * +
| * |
1 + * +
| * ----- -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ - - - - - -
0 + * +
| * |
-1 + * +
| * |
-2 + * +
| * |
-3 + * +
| * *
-4 + *-*-*--+--+----+-+--+--+ -+--+-+-+-+ - *
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
-4 -2 0 2 4
The two lines intersect at approximately (1, -1/3). Therefore, the solution to the system of equations is x = 1 and y = -1/3.