Question

The following system of linear equations is solved by graphing them on the coordinate plane:

y = 3x - 2
y = -3/5x - 1
Which ordered pair is the best approximation of the solution to the system?
a) (-1, 0)
b) (0, -1)
c) (2, 4)

Answer 1

To solve the system of linear equations y = 3x - 2 and y = -3/5x - 1, we can graph the two equations on the coordinate plane to find the point of intersection. The best approximation of the solution is the ordered pair (-1, 0).

Step-by-step explanation:

To solve the system of linear equations y = 3x - 2 and y = -3/5x - 1, we can graph the two equations on the coordinate plane and find the point where they intersect. The best approximation of the solution to the system is the ordered pair (-1, 0), which is option a. To graph the equations, we can assign different values to x and solve for y. Then we plot the points and draw a line through them:

For the first equation, when x = -1, y = 3(-1) - 2 = -3 - 2 = -5. So we have the point (-1, -5).

For the second equation, when x = -1, y = -3/5(-1) - 1 = 3/5 - 1 = -2/5. So we have the point (-1, -2/5).

When we graph these points and draw the lines, we see that they cross at approximately (-1, 0), making it the best approximation of the solution.