Question

Y = 2x - 1y=9x + 6Does this system have a solution? If so, what is the solution? Explain. helppp

Answer 1

x = - 1, y = - 3

Explanation:

y = 2x - 1 → (1)

y = 9x + 6 → (2)

substitute y = 9x + 6 into (1)

9x + 6 = 2x - 1 ( subtract 2x from both sides )

7x + 6 = - 1 ( subtract 6 from both sides )

7x = - 7 ( divide both sides by 7 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (1)

y = 2(- 1) - 1 = - 2 - 1 = - 3

solution is (- 1, - 3 )

Answer 2

The given system is,

`\begin{gathered} y=2x-1 \\ y=9x+6 \end{gathered}`

From the first equation, we have,

`\begin{gathered} 2x=y+1 \\ x=(y+1)/(2) \end{gathered}`

Substituting this value in the second equation, we have,

`\begin{gathered} y\text{ =9(}(y+1)/(2))+6 \\ 2y=9y+9+12 \\ -7y=21 \\ y=-3 \end{gathered}`

Therefore,

`x=(-3+1)/(2)=-(2)/(2)=-1`

Thus, y = -3 and x = -1

Thus, the system has solution.