How do you solve the following linear system: -x+2y=-6 , 5x-2y=-35 ?

1 Answer
Apr 26, 2018

Isolate x , replace x with the expression equal to x , isolate y, and then use the value of y to solve for x.

Explanation:

Isolate x in the simplest manner possible:

Equation 1: -x + 2y =-6
Equation 2: 5x - 2y =-35

  1. -x + x + 2y = - 6 + x
  2. 2y + 6 = -6 + x +6
  3. 2y + 6 = x

Substitute the expression in step 3 in for x in equation 2

2y+6=x->5[2y+6]-2y=-35

Distribute 5 onto 2y+6 to get the equation,

10y+30-2y=-35

Which becomes...

8y = -65

Now isolate y ...

(8y)/8 = -65/8

y = -65/8

... and use the value of y to find x !

-x - 2((-65)/8) = -6

-2*-65/8 =130/8=16.25
-x=-6+130/8-> -x=82/8

There aren't negative signs on both sides of the equation, so the value of x is in turn, positive, and the right side of the equation, becomes negative:

x= -82/8, y=-65/8

Since these are linear systems, these are the only solutions to the system. You can always rewrite both equations in terms of y and graph them. The x and y coordinates where the two lines intersect one another (-82/8,-65/8), are the solutions to the system.

Graph these:
y=5/2x+35/2
y = 1/2x-3