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Ierofanga [76]
3 years ago
8

Homework: 5.1 Systems of Linear Equations

Mathematics
1 answer:
Klio2033 [76]3 years ago
7 0

Answer:

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

x=8,\:y=5

Step-by-step explanation:

Given the system of linear equations

7x-y=51

x+3y=23

solving by the elimination method

\begin{bmatrix}7x-y=51\\ x+3y=23\end{bmatrix}

\mathrm{Multiply\:}x+3y=23\mathrm{\:by\:}7\:\mathrm{:}\:\quad \:7x+21y=161

\begin{bmatrix}7x-y=51\\ 7x+21y=161\end{bmatrix}

7x+21y=161

-

\underline{7x-y=51}

22y=110

so

\begin{bmatrix}7x-y=51\\ 22y=110\end{bmatrix}

now solving for y

22y=110

\mathrm{Divide\:both\:sides\:by\:}22

\frac{22y}{22}=\frac{110}{22}

y=5

\mathrm{For\:}7x-y=51\mathrm{\:plug\:in\:}y=5

7x-y=51

7x-5=5

7x=56

\mathrm{Divide\:both\:sides\:by\:}7

\frac{7x}{7}=\frac{56}{7}

x=8

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

x=8,\:y=5

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