Graph the system below and write its solution. y = -1/2 x -1-2 + y = -6.. there is also "no solution" or "infinite solution" answers.

Accepted Solution

Answer: See the graph attached. It has one solution: (6,-4)Step-by-step explanation: The slope-intercept form of a line is: [tex]y=mx+b[/tex] Where m is the slope and b is the intersection of the line with the y-axis. Given the first equation  [tex]y =\frac{-1}{2}x -1[/tex] You can identify that: b=-1 Substitute y=0 to find the intersection with the x-axis [tex]0 =\frac{-1}{2}x -1\\1(-2)=x\\x=-2[/tex] This line passes through the points (0,-1) and (-2,0) Given the second equation: [tex]-2 + y = -6[/tex] Solve for y: [tex]y = -6+2\\y=-4[/tex] It passes through the point (0,-4). Now, you can graph. See the figure attached. It has one solution,which is the point of intersection of both lines:  (6,-4)