Solve the system of equations by graphing

  2x+y=3 and 4x+4y=8
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We appear to have two systems of equations, but the method for solving either is essentially the same.

First we make the equations into the form y=.

The first system: y=2x+7, 4y=-8-4x or y=-2-x. 

The second system: y=3-2x, y=2-x.

Now we draw the graphs. We can put them all on to the same graph, but we should label all the line graphs so as not to get them mixed up. To draw straight line graphs, we find the x and y intercepts and draw a line joining and passing through them. System 1: y=2x+7: y-int (x=0) is 7, x-int (y=0) is -3.5; y=-2-x: y-int is -2, x-int is -2; system 2: y=3-2x: y-int is 3, x-int is 2; y=2-x: y-int is 2, x-int is 2.

For each system, draw a line through the intercepts for each equation. System 1: join 7 on the y-axis to -3.5 on the x axis and join -2 on y to -2 on x; system 2: join 3 on y to 2 on x and join 2 on y to 2 on x. Label the lines with their equations.

You should find that in system 1 the lines cross at the solution to 2x+7=-2-x, 3x=-9, so x=-3 and y=1 (-2+3 or -6+7); and in system 2 3-2x=2-x, x=1 and y=1. The points where the lines cross are therefore (-3,1) for system 1 and (1,1) for system 2. These are the graphical representations of the solutions of the two systems of equations.

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