Question

How do you solve `-x + 3y =10`, `x+y=2` by graphing and classify the system?

Answer 1

Two unknowns and two equations `x=-1` and `y=3`

Explanation:

Add these equations first:
`-x+x+3y+y=10+2`
`4y=12`
`y=3`
If `y=3` what is x?
`-x+3*3=10`
`-x=10-9`
`x=-1`

The first equation (GRAPH) graph{(10+x)/3 [-10, 10, -5, 5]}

The second equation (GRAPH) graph{2-x [-10, 10, -5, 5]}

Together: graph{(-x+3y-10)(x+y-2)=0 [-10, 10, -5, 5]}

Answer 2

Se below for solution by (only) graphing

Explanation:

Pick a pair of sample points for the equation `color(green)(-x+3y=10)`
#color(white)("XXX"){: (color(green)(ul(x)),color(green)(ul(y))), (color(green)(5),color(green)(5)), (color(green)(2),color(green)(4)) :}#

Pick a pair of sample points for the equation `color(magenta)(x+y=2)`
#color(white)("XXX"){: (color(magenta)(ul(x)),color(magenta)(ul(y))), (color(magenta)(0),color(magenta)(2)), (color(magenta)(2),color(magenta)(0)) :}#

Plot the points for each equation and draw a line through the pair for each:

Read the solution as the intersection point directly from the graph:
`color(white)("XXX")(x,y)=(-1,3)`