Question

Graph the system below and write the solution { y = 1/2x - 1

Answer 1

Answer:

• The solution of the system is x = 2, y = 0
• The graph of the system is in the file attached.

Step-by-step explanation:

To graph the system follow these steps:

1) Equation 1: y = (1/2)x - 1

That is a linear equation, so you can use some features to graph it.

• The slope intercept form of a linear equation is y = mx + b where m is the slope and b is the y-intercept.

• So, from that, the slope of y = (1/2)x - 1 is m = 1/2, and the y-intercept is b = - 1. That means that (0, -1) is one point of the line.

• The x-intercept is the value of x when y = 0:

        ⇒ 0 = (1/2)x - 1 ⇒ (1/2)x = 1 ⇒ x = 2.

        So, a second point of the line is (2,0)

• The blue line of the graph attached shows the line that joins the points (0, -1) and (2,0).

2) Equation 2: 2x + y = 4

That is also the equation of a line. In this case, you can first solve for y and then follow the same steps described above to graph the function.

• y = 4 - 2x

• slope, m = - 2

• y-intercept: b = 4 ⇒ (0, 4)

• x-intercept: y = 0 = 4 - 2x ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)

The green line in the same graph shows the line that joins the points (0,4) and (2,0).

3) Solution

In the graph you can see that the solution of the system is the point where the lines intersect each other. That point has coordinates (2,0).

That point belongs to both equations, that is why it is the solution of the system. So, the solution is:

• x = 2
• y = 0