Question

Solve the system using elimination. x + 2y = –6 3x + 8y = –20 (–4, –1) (–4, 4) (–1, –4) (3, 1)

Answer 1

$x + 2y = - 6 > > > 3x = - 18 - 6y$
$- 18 - 6y + 8y = - 20 > > > 2y = - 2 > > y = - 1$
so x=4

Answer 2

Answer:  The required solution is  x = -4  and  y = -1.

Step-by-step explanation:  We are given to solve the following system of equations by the method of Elimination :

$x+2y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+8y=-20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 3 , we have

$3(x+2y)=-6\times3\\\\\Rightarrow 3x+6y=-18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Subtracting equation (iii) from equation (ii), we get

$(3x+8y)-(3x+6y)=-20-(-18)\\\\\Rightarrow 2y=-20+18\\\\\Rightarrow 2y=-2\\\\\Rightarrow y=-\dfrac{2}{2}\\\\\Rightarrow y=-1.$

From equation (i), we get

$x+2\times(-1)=-6\\\\\Rightarrow x-2=-6\\\\\Rightarrow x=-6+2\\\\\Rightarrow x=-4.$

Thus, the required solution is  x = -4  and  y = -1.