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

1 Answer
CM2607
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 ...

8y8=−658

y=−658

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

−x−2(−658)=−6

−2⋅−658=1308=16.25
−x=−6+1308→−x=828

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=−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 y and graph them. The x and y coordinates where the two lines intersect one another (−828,−658), are the solutions to the system.

Graph these:
y=52x+352
y=12x−3

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