Question

1.1. Which statement explains why the two systems of equations below have thesame solution?A6x + 8y = -102x - 5y = 12B8x + 3y = 212x + 16y = -20

Answer 1

Let:

`\begin{gathered} 6x+8y=-10_{\text{ }}(1) \\ 2x-5y=12_{\text{ }}(2) \\ 8x+3y=2_{\text{ }}(3) \\ 12x+16y=-20_{\text{ }}(4) \end{gathered}`
`\begin{gathered} (4)=2(1) \\ so\colon \\ 2(6x+8y)=2(-10)\equiv12x+16y=-20 \\ 12x+16y=-20\equiv12x+16y=-20 \end{gathered}`

Therefore, (4) is a Scalar Multiple of (1).

`\begin{gathered} (1)+(2) \\ 6x+2x+8y-5y=-10+12 \\ 8x+3y=2\equiv(3) \\ so\colon_{} \\ (1)+(2)\equiv(3) \end{gathered}`

Therefore, (3) is a linear combination of (1) and (2)