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

Step-by-step 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

$y = - \frac{10}{7}$

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

$x = 6 + 2 \times ( - \frac{10}{7} )$

solve the equation for x

$x = \frac{22}{7}$

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

$(\frac{22}{7} . - \frac{10}{7} )$

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

$(x.y) \: \: ( \frac{22}{7} . - \frac{10}{7} )$

This is the solution

Marnie out!

Answer 2

Answer:

$x=2y+6$

Step-by-step 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:

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