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*3\\\\\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=-(2)/(2)\\\\\Rightarrow y=-1.`

From equation (i), we get

`x+2*(-1)=-6\\\\\Rightarrow x-2=-6\\\\\Rightarrow x=-6+2\\\\\Rightarrow x=-4.`

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