Question

For the following system, if you isolated x in the first equation to use the substitution method, what expression would you substitute into the second equation? −x + 2y = −6 3x + y = 8

Answer 1

Explanation:

Start by solving the equation for x (☓)

`- x + 2y = 6 \\ \: \: \: \: \: 3 + y = 8`

`x = 6 + 2y`

Substitute the given value of x for the equation 3 + y = 8

`3(6 + 2y) + y = 8`

solve the equation for y

`y = - (10)/(7)`

substitute the given value of y into the equation x = 6 + 2

`x = 6 + 2 * ( - (10)/(7) )`

solve the equation for x

`x = (22)/(7)`

The possible solution of the system is the ordered pair (x,y)

`((22)/(7) . - (10)/(7) )`

The dot (.) in the center is supposed to be a comma but the scientific keyboard does not support a comma

`(x.y) \: \: ( (22)/(7) . - (10)/(7) )`

This is the solution

Marnie out!

Answer 2

`x=2y+6`

Explanation:

So we have the system:

`-x+2y=-6\\3x+y=8`

If we isolate the x-variable in the first equation:

`-x+2y=-6`

Subtract 2y from both sides:

`-x=-6-2y`

Divide both sides by -1:

`x=2y+6`

Therefore, we would substitute the above into the second equation:

`3x+y=8\\3(2y+6)+y=8`

The answer is 2y+6

Further notes:

To solve for the system, distribute:

`6y+18+y=8`

Simplify:

`7y+18=8`

Subtract:

`7y=-10`

Divide:

`y=-10/7\approx-1.4286`

Now, substitute this value back into the isolated equation:

`x=2(-10/7)+6\\x=-20/7+42/7\\x=22/7\approx3.1429`