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

Apr 12, 2017

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

#### Explanation:

$- x + x + 3 y + y = 10 + 2$
$4 y = 12$
$y = 3$
If $y = 3$ what is x?
$- x + 3 \cdot 3 = 10$
$- x = 10 - 9$
$x = - 1$

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]}

Apr 12, 2017

Se below for solution by (only) graphing

#### Explanation:

Pick a pair of sample points for the equation $\textcolor{g r e e n}{- x + 3 y = 10}$
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 $\textcolor{m a \ge n t a}{x + y = 2}$
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:
$\textcolor{w h i t e}{\text{XXX}} \left(x , y\right) = \left(- 1 , 3\right)$