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Vanyuwa [196]
3 years ago
10

Solve the system using substitution. Check your solution. 2x - y= 65 5y = x

Mathematics
1 answer:
lyudmila [28]3 years ago
3 0

Answer:

The solutions to the system of equations are:

x=\frac{325}{9},\:y=\frac{65}{9}

Step-by-step explanation:

Given the system of the equations

\begin{bmatrix}2x-y=65\\ 5y=x\end{bmatrix}

isolate 'x' for 2x-y

2x-y=65

Add y to both sides

2x-y+y=65+y

2x=65+y

Divide both sides by 2

\frac{2x}{2}=\frac{65}{2}+\frac{y}{2}

x=\frac{65+y}{2}

\mathrm{Subsititute\:}x=\frac{65+y}{2}

isolate 'y' for  5y=\frac{65+y}{2}

5y=\frac{65+y}{2}

10y=65+y

subtract y from both sides

10y-y=65+y-y

9y=65

Divide both sides by 9

\frac{9y}{9}=\frac{65}{9}

y=\frac{65}{9}

\mathrm{For\:}x=\frac{65+y}{2}

\mathrm{Subsititute\:}y=\frac{65}{9}

x=\frac{65+\frac{65}{9}}{2}

x=\frac{325}{9}

The solutions to the system of equations are:

x=\frac{325}{9},\:y=\frac{65}{9}

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