# How do solve the following linear system?: # -7x+y=-19 , -2x+3y=-1 #?

##### 1 Answer

#### Explanation:

#{(-7x+y=-19),(-2x+3y=-1):}#

Notice that the single variable

Taking the first equation

#color(blue)(y=7x-19)#

We now have an expression equal to

#-2x+3color(blue)y=-1" "=>" "-2x+3color(blue)((7x-19))=-1#

We can now solve this equation, since it's entirely in terms of

#-2x+(21x-57)=-1#

Combining the

#19x-57=-1#

#19x=56#

Then

#color(red)(x=56/19#

Now we can plug this into either equation to find the value of

#-2color(red)x+3y=-1#

#-2color(red)((56/19))+3y=-1#

#-112/19+3y=-1#

Multiplying everything by

#-112+57y=-19#

So

#57y=93#

#y=93/57#

Both of these are divisible by

#y=(31xx3)/(19xx3)#

#color(green)(y=31/19)#

So the solution is the point

The graphs of the the lines

graph{(-7x+y+19)(-2x+3y+1)=0 [-10.61, 17.87, -4.8, 9.44]}

They do!