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gayaneshka [121]
3 years ago
5

HELP! I NEED THE ANSWER ASAP!!!!!

Mathematics
1 answer:
vladimir1956 [14]3 years ago
7 0

Answer:

The solution to the given system of equations is (-2, -2).

Step-by-step explanation:

The given system of equations is,

2<em>x</em> + <em>y</em> = -6               .......(1)

-8<em>x</em> + 2<em>y</em> = 12            ......(2)

Now, we will make the coefficients of either <em>x</em> or <em>y</em> as opposites.

In the above system of equations, we will make the coefficients of <em>x</em> as opposites.

Multiplying equation (1) by '4' and equation (2) by '1', we get

8<em>x</em> + 4<em>y</em> = -24         .......(3)

-8<em>x</em> + 2<em>y</em> = 12          .......(4)

Now, we will add the equations (3) and (4).

  (8<em>x</em> + 4<em>y</em>) + (-8<em>x</em> + 2<em>y</em>) = -24 + 12

⇒8<em>x</em> + 4<em>y</em> - 8<em>x</em> + 2<em>y</em> = -12

⇒6<em>y</em> = -12

⇒<em>y</em> = \frac{-12}{6}

⇒<em>y</em> = -2

Now, substituting the value of <em>y</em> in equation (1), we get

  2<em>x</em> + (-2) = -6

⇒2<em>x</em> - 2 = -6

⇒2<em>x</em> = -6+2

⇒2<em>x</em> = -4

⇒<em>x</em> = \frac{-4}{2}

⇒<em>x </em>= -2

∴ <em>x</em> = -2; <em>y</em> = -2 is the solution of the given system of equations.

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