Question

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite numberof solutions. If the system has one solution, find the solution.- 4x + 2y = - 12- 2x+y=-6

Answer 1

No Solution

Step-by-step explanation

Given:

`\begin{gathered} -4x+2y=-12............equ1 \\ -2x+y=-6...............equ2 \end{gathered}`

Solve by substitution

from equation 2:

`\begin{gathered} -2x+y=-6 \\ add\text{ }2x\text{ }to\text{ }both\text{ }sides \\ -2x+y+2x=2x-6 \\ y=2x-6..................equ3 \end{gathered}`

Substitute equation 3 into equation 1

`\begin{gathered} -4x+2y=-12 \\ -4x+2(2x-6)=-12 \\ -4x+4x-12=-12 \\ -12=-12 \\ =0 \end{gathered}`

Hence, the system has no solution.