Final answer:
To solve the system of equations by graphing y = -3x + 6 and 2y = 10x - 36, one must graph both equations on the same coordinate plane to find the point of intersection; this point will be the solution to the system.
Step-by-step explanation:
To solve the system of equations by graphing y = -3x + 6 and 2y = 10x - 36, let's first rewrite the second equation in the form y = mx + b by dividing both sides by 2 to get y = 5x - 18.
Next, we graph both equations on the same set of axes.
- For the first equation: the y-intercept is 6 (where x = 0), and the slope is -3. From the y-intercept (0,6), move down 3 units and to the right 1 unit to find another point (1,3). Connect these points to draw the line.
- For the second equation: the y-intercept is -18 (where x = 0), and the slope is 5. From the y-intercept (0,-18), move up 5 units and to the right 1 unit to find another point (1,-13). Connect these points to draw the line.
The point where both lines intersect is the solution to the system of equations. If the lines intersect, that point gives the values of x and y that satisfy both equations