Question

Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many solutions.How many solutions does the system of equations have?y=11x-6y=-6x+11

Answer 1

one​ solution

Step-by-step explanation:

Given the system of equations:

`\begin{gathered} y=11x-6 \\ y=-6x+11 \end{gathered}`

Equating the two expressions of y:

`\begin{gathered} 11x-6=-6x+11 \\ 11x+6x=11+6 \\ 17x=17 \\ x=(17)/(17) \\ x=1 \end{gathered}`

Next, solve for y:

`\begin{gathered} y=11x-6 \\ =11(1)-6 \\ =11-6 \\ y=5 \end{gathered}`

Thus, we conclude that the system of equations has exactly one solution (1, 5).