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