Solve by graphing. 3x+y=5 -x+2y=-4I have no clue as to how to do this problem.

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lemjay | High School Teacher | (Level 3) Senior Educator

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The given system of equations are:

`3x+y=5`

`-x+2y=-4`

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`

                    `x=5/3`

                    `x=1.67`

And to find the y-intercept, set x=0 and solve for y.

`x=0` ,  `3(0) + y= 5`

                `0 + y=5`

                     `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`

                          `x= 4`

And, set x=0 and solve for y.

`x=0` ,   `-(0) + 2y=-4`

                        `2y=-4`

                           `y=-2`

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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