Question

graph these equations:
$y = 2x - 1$
$x = 1$
click to select points on the graph.
how many solutions does the system of equations have?

Explanation:

Step1: Analyze the first equation \( y = 2x - 1 \)

This is a linear equation in slope - intercept form (\( y=mx + b \), where \( m = 2 \) is the slope and \( b=- 1 \) is the y - intercept). We can find two points on this line. When \( x = 0 \), \( y=2(0)-1=-1 \). When \( x = 1 \), \( y=2(1)-1 = 1 \).

Step2: Analyze the second equation \( x = 1 \)

This is a vertical line that passes through all points with \( x \)-coordinate equal to 1.

Step3: Find the intersection point

To find the solution of the system, we substitute \( x = 1 \) into the first equation \( y=2x - 1 \). When \( x = 1 \), \( y=2(1)-1=1 \). So the two lines intersect at the point \( (1,1) \). A system of linear equations has a solution at the intersection point of their graphs. Since these two lines (one with slope 2 and y - intercept - 1, and one vertical line \( x = 1 \)) intersect at exactly one point, the system of equations has one solution.

Answer:

The system of equations has 1 solution.