Question

Use substitution to solve the system of equations. How many solutions are there?1/2x-1/3y=5x=2/3y+10No solution One solution Infinity many It’s not possible to determine the numbers of solutions

Answer 1

The set of equations is,

`\begin{gathered} (1)/(2)x-(1)/(3)y=5 \\ x=(2)/(3)y+10 \end{gathered}`

Substituting the values of x from second equation in the first one, we have,

`\begin{gathered} (1)/(2)((2)/(3)y+10)-(y)/(3)=5 \\ (2y)/(6)+5-(y)/(3)=5 \\ (2y)/(6)-(y)/(3)=0 \end{gathered}`

Further,

`\begin{gathered} (6y-6y)/(18)=0 \\ \end{gathered}`

Hence the solution is y = 0 , substituting this value for x, we get, x = 10.