Question

The system of equations y = negative one-half x + 4 and y = 2x – 1 is shown on the graph below. On a coordinate plane, 2 lines intersect at (2, 3). According to the graph, what is the solution to this system of equations?

a. (2, 3)
b. (3, 2)
c. (–1, 4)
d. (4, –1)

Answer 1

The solution to the system of equations y = -½x + 4 and y = 2x – 1, which intersect at a point on the graph, is (2, 3). The correct answer is option (a).

Step-by-step explanation:

The system of equations given by y = -½x + 4 and y = 2x – 1 intersects at a point on the graph. This point represents the solution to the system of equations, where both equations have the same x and y values. According to the information provided, the lines intersect at the point (2, 3). This means that when x is 2, both equations will yield a y-value of 3. Since this is the point of intersection, the correct solution to the system of equations is (2, 3).

To verify, we can substitute x with 2 in both equations and see if we get y as 3. For the first equation:

• y = -½(2) + 4 = -1 + 4 = 3

And for the second equation:

• y = 2(2) - 1 = 4 - 1 = 3

Since both equations yield a y-value of 3 when x is 2, this confirms that the solution (2, 3) is correct for the system.