ddsonic342
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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

Respuesta :

xKelvin

Answer:

[tex]x=2y+6[/tex]

Step-by-step explanation:

So we have the system:

[tex]-x+2y=-6\\3x+y=8[/tex]

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

[tex]-x+2y=-6[/tex]

Subtract 2y from both sides:

[tex]-x=-6-2y[/tex]

Divide both sides by -1:

[tex]x=2y+6[/tex]

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

[tex]3x+y=8\\3(2y+6)+y=8[/tex]

The answer is 2y+6

Further notes:

To solve for the system, distribute:

[tex]6y+18+y=8[/tex]

Simplify:

[tex]7y+18=8[/tex]

Subtract:

[tex]7y=-10[/tex]

Divide:

[tex]y=-10/7\approx-1.4286[/tex]

Now, substitute this value back into the isolated equation:

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

marnie16

Step-by-step explanation:

Start by solving the equation for x (☓)

[tex] - x + 2y = 6 \\ \: \: \: \: \: 3 + y = 8[/tex]

[tex]x = 6 + 2y[/tex]

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

[tex]3(6 + 2y) + y = 8[/tex]

solve the equation for y

[tex]y = - \frac{10}{7} [/tex]

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

[tex]x = 6 + 2 \times ( - \frac{10}{7} )[/tex]

solve the equation for x

[tex]x = \frac{22}{7} [/tex]

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

[tex] (\frac{22}{7} . - \frac{10}{7} )[/tex]

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

[tex](x.y) \: \: ( \frac{22}{7} . - \frac{10}{7} )[/tex]

This is the solution

Marnie out!

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