Solve this system using elimination (20 POINTS) 4x-7y=3 x-7y=-15

Mathematics

1 answer:

stiv31 [10]2 years ago

4 0

Answer:

x = 6, y =3

Step-by-step explanation:

4x-7y=3

x-7y=-15

Multiply the first equation by -1

-4x+7y=-3

Then add this to the second equation to eliminate y

-4x+7y=-3

x-7y=-15

------------------

-3x +0y = -18

-3x = -18

Divide by -3

-3x/-3 = -18/-3

x = 6

Now find y

x -7y = -15

6 -7y = -15

Subtract 6 from each side

6-7y-6 = -15-6

-7y = -21

Divide by -7

-7y/-7 = -21/-7

y =3

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Select the two values of x that are roots of this equation

Jet001 [13]

<h2>Hello!</h2>

The answers are:

B. $\frac{-3-\sqrt{29}}{2}$

C. $\frac{-3+\sqrt{29}}{2}$

We can use the quadratic equation to find the two values of x that are roots of the given equation. We must remember that most of the quadratic equations have two roots, however, we could find quadratic equations with just one root or even with no roots, at least in the real numbers.

Quadratic equation:

$\frac{-b+-\sqrt{b^{2}-4ac} }{2a}$

So,

From the given equation we have:

$a=1\\b=3\\c=-5$

Substituting it into the quadratic equation to find the roots, we have:

$\frac{-b+-\sqrt{b^{2}-4ac} }{2a}=\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}\\\\\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}=\frac{-3+-\sqrt{9+20} }{2}\\\\\frac{-3+-\sqrt{29}}{2}$