Answer:
The solution of the system of equation is x=-1 and y=3 or (-1,3).
Step-by-step explanation:
Consider the provided system of equations.
[tex]-2x=2y-4\ and\ 2x-y=-5[/tex]
The above function is a linear function.
The graph of a linear function is a straight line.
To draw the graph, find any two points which satisfy the equation and draw a line passing through these points.
Substitute x = 0 in [tex]-2x=2y-4[/tex].
[tex]-2(0)=2y-4[/tex]
[tex]4=2y[/tex]
[tex]y=2[/tex]
Coordinate which satisfy the function (0,2)
Substitute y = 0 in [tex]-2x=2y-4[/tex].
[tex]-2x=2(0)-4[/tex]
[tex]-2x=-4[/tex]
[tex]x=2[/tex]
Coordinate which satisfy the function (2,0)
Draw a straight line passing through the points (0.2) and (2,0).
Similarly.
Substitute x = 0 in [tex]2x-y=-5[/tex].
[tex]2(0)-y=-5[/tex]
[tex]y=5[/tex]
Coordinate which satisfy the function (0,5)
Substitute y = 0 in[tex]2x-y=-5[/tex]..
[tex]2x-0=-5[/tex].
[tex]2x=-5[/tex]
[tex]x=-2.5[/tex]
Coordinate which satisfy the function (-2.5,0)
Draw a straight line passing through the points (0.5) and (-2.5,0).
The required graph is shown below.
The solution of system of equation is the point where both the lines intersect.
From the graph we can concluded that both the lines intersect at (-1,3).
Hence, the solution of the system of equation is x=-1 and y=3 or (-1,3).
