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 :

The set of equations is,

[tex]\begin{gathered} \frac{1}{2}x-\frac{1}{3}y=5 \\ x=\frac{2}{3}y+10 \end{gathered}[/tex]

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

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

Further,

[tex]\begin{gathered} \frac{6y-6y}{18}=0 \\ \end{gathered}[/tex]

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

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