1)
First step is to get the x on the right side of the equal sign and the y on the left without any coefficients.
For the first equation: 6x + 3y = 6, we subtract 6x from both sides and get:
3y = - 6x + 6, then we divide all expressions by 3:
3y/3 = -6x/3 + 6/3, which gives us the first equation in general form: y = - 2x + 2.
We do the same for the next equation:
2x + y = 2, we subtract 2x from both sides of the equation:
y = - 2x + 2, which gives us the second equation in general form
We then have to graph the equations. I'd suggest making a table of values. Then draw up your axies plot the points, join the dots and continue the line to the end of your axies.
y = - 2x + 2:
x -3 -2 -1 0 1 2 3
y 8 6 4 2 0 -2 -4
Because both equations are exactly the same, they do not cross at one point.
6)
We do the same as we did above, we move the x on the right side of the =, the y on the left and without any coefficients.
x - y = -2, the first thing we do is subtract x from both sides of the equation:
-y = -x - 2, the second thing we do is divide every expression by -1 to remove the - sign from the y;
-y/-1 = -x/-1 -2/-1, this gives us the general form of the equation:
y = x + 2,
We do the same with the second equation by following the steps above:
2x + y = 5, we subtract 2x from both sides of the equation:
y = -2x + 5.
We then graph the equations. We draw up our table of values, plot the points, join the dots and continue the line to the end of your axies:
y = x + 2:
x -3 -2 -1 0 1 2 3
y -1 0 1 2 3 4 5
y = - 2x + 5:
x -3 -2 -1 0 1 2 3
y 8 6 4 2 0 -2 -4
All you have to do is use the tables above to plot the points on your graph and then draw your line, making sure it intersects all the points