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The given system of equations are:
To solve by graphing, graph each equation.
Note that to graph linear equation, at least two points are needed. To determine the points, use the x and y intercepts.
For 3x+y=5, to find its x-intercept set y=0 and solve for x.
`y=0` , `3x + 0 = 5`
`3x = 5`
And to find the y-intercept, set x=0 and solve for y.
`x=0` , `3(0) + y= 5`
`0 + y=5`
So for the first equation, the two points are `(1.67,0)` and `(0,5)` . Plot these points. Connect them and extend the line on both ends.
For -x+2y=4, to determine the intercepts do the same steps.
Set y=0 and solve for x.
`y=0` , `-x + 2(0)=-4`
`-x = -4`
And, set x=0 and solve for y.
`x=0` , `-(0) + 2y=-4`
Then, plot these two points (4,0) and (0, -
2). Connect them and extend the line on both its ends.
Thus, the graph of the two equations are:
(Blue-graph of 3x+y=5, Green-graph of -x+2y=4)
The solution of the system of equations is the intersection point of the two lines.
Base on the graph above, the solution is (2, -1).
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