Question

Here is a system of equations:

3x - y = 17
x + 4y = 10
Solve the system by graphing the equations (by hand or using technology). Write your answer in the following format: (x, y) with no spaces.
a) (5, 2)
b) (4, 3)
c) (3, 4)
d) (2, 5)

Answer 1

To solve the system of equations 3x - y = 17 and x + 4y = 10 by graphing, plot the lines for each equation and find the point of intersection. The solution to the system is the point where the two lines intersect. By graphing the equations, we can see that the point of intersection is b. (4, 3).

Step-by-step explanation:

To solve the system of equations 3x - y = 17 and x + 4y = 10 by graphing, we need to first graph each equation on the same coordinate plane. Let's start with the first equation:

For the equation 3x - y = 17, we can rearrange it to y = 3x - 17. Now we can choose some values for x and calculate the corresponding values for y. For example, when x = 0, y = 3(0) - 17 = -17. When x = 1, y = 3(1) - 17 = -14. Plot these points (0, -17) and (1, -14) and draw a line passing through them.

Next, let's graph the second equation x + 4y = 10. We can rearrange it to y = (10 - x)/4. Choose some values for x and calculate the corresponding values for y. Plot these points and draw a line passing through them.

The solution to the system is the point where the two lines intersect. By graphing the equations, we can see that the point of intersection is (4, 3).