u can also solve the system of equations this way:

x+y=3

x+y=-1

x+y=3

-x-y=1

0y=4

y=undefined

no solution

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4x+2y=10

y=4

4x+8=10

4x=2

x=1/2

(1/2,4)

x+y=3

x+y=-1

is inconsistent, as x+y cannot be equal to 3 and to -1 at once. To illustrate this draw the line x+y=3, which passes through the points (3,0) and (0,3), and the line x+y=-1, which passes through the points (-1,0) and (0,-1). These lines are parallel, hence they have no common points.

To solve the second system

4x+2y=10

y=4

draw the line 4x+2y=10. To do that, you need to find two points on this line. Set x=0, then y=5 and the first point is at (0,5). Then set x=1, then y = 3 and the second point is at (1,3). Mark these points on the xy-plane and draw a line through them.

The line y=4 is a horizontal line passing through the point (0,4).

Obviously the both lines intersect at (1/2, 4). the solution is

x=1/2

y=4

2) 4x+2y=10 change to 2x+y=5 rearrange to y=-2x+5. Graph this and then graph y=4(line 4 up and parallel to x axis.) Where they cross is the solution. Plot (0,4), (1,4),(2,4) and draw straight line.