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

1 Answer
CM2607
Apr 26, 2018

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

Explanation:

Isolate xx in the simplest manner possible:

Equation 1: -x + 2y =-6−x+2y=−6
Equation 2: 5x - 2y =-355x−2y=−35

  1. -x + x + 2y = - 6 + x−x+x+2y=−6+x
  2. 2y + 6 = -6 + x +6 2y+6=−6+x+6
  3. 2y + 6 = x2y+6=x

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

2y+6=x->5[2y+6]-2y=-352y+6=x→5[2y+6]−2y=−35

Distribute 55 onto 2y+62y+6 to get the equation,

10y+30-2y=-3510y+30−2y=−35

Which becomes...

8y = -658y=−65

Now isolate yy ...

(8y)/8 = -65/88y8=−658

y = -65/8y=−658

... and use the value of yy to find xx !

-x - 2((-65)/8) = -6−x−2(−658)=−6

-2*-65/8 =130/8=16.25−2⋅−658=1308=16.25
-x=-6+130/8-> -x=82/8−x=−6+1308→−x=828

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

x= -82/8, y=-65/8x=−828,y=−658

Since these are linear systems, these are the only solutions to the system. You can always rewrite both equations in terms of yy and graph them. The x and y coordinates where the two lines intersect one another (-82/8,-65/8)(−828,−658), are the solutions to the system.

Graph these:
y=5/2x+35/2y=52x+352
y = 1/2x-3y=12x−3

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