The given system of equations is [tex]y=-4x-5[/tex] and [tex]y=x+5[/tex]
We need to determine the solution to the system of equations.
Plotting the equation [tex]y=-4x-5[/tex] :
The equation [tex]y=-4x-5[/tex] can be plotted in the graph using the x and y intercepts.
When [tex]x=0[/tex], the equation becomes [tex]y=-5[/tex]
When [tex]y=0[/tex], the equation becomes [tex]x=-1.25[/tex]
Hence, joining these coordinates (0,-5) and (-1.25, 0), we get the line for the equation [tex]y=-4x-5[/tex]
Plotting the equation [tex]y=x+5[/tex]:
The equation [tex]y=x+5[/tex] can be plotted in the graph using the x and y intercepts.
When [tex]x=0[/tex], the equation becomes [tex]y=5[/tex]
When [tex]y=0[/tex], the equation becomes [tex]x=-5[/tex]
Hence, joining these coordinates (0,5) and (-5,0), we get the line for the equation [tex]y=x+5[/tex]
Solution of the system of equations:
The solution of the system of equations is the point of intersection of these two lines.
Thus, from the graph, the lines intersect at the point (-2,3)
Hence, the solution to the system of equations is (-2,3)
