Question

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

Answer 1

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`