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crimeas [40]
3 years ago
12

Solve the system of linear equations. Give your solution as an ordered pair, either as a fraction or a decimal with at least 3 d

ecimal places.
1/8x - 1/2y = 1
1/3x + 1/8y = -1
Mathematics
1 answer:
valina [46]3 years ago
6 0

Answer:

\left(-\dfrac{72}{35},-\dfrac{88}{35}\right)

Step-by-step explanation:

\textsf{Equation 1}: \quad \dfrac{1}{8}x-\dfrac{1}{2}y=1

\textsf{Equation 2}: \quad \dfrac{1}{3}x+\dfrac{1}{8}y=-1

Multiply Equation 1 by 8:

\textsf{Equation 1}: \quad 8\left(\dfrac{1}{8}x-\dfrac{1}{2}y=1\right)\implies x-4y=8

Multiply Equation 2 by 32:

\textsf{Equation 2}: \quad 32\left(\dfrac{1}{3}x+\dfrac{1}{8}y=-1\right)\implies \dfrac{32}{3}x+4y=-32

Add the new equations together to eliminate y:

\begin{array}{ l r c r c r}& x & - & 4y & = & 8\\\\+ & \dfrac{32}{3}x & + & 4y & = & -32\\\\\cline{1-6}\\& \dfrac{35}{3}x & & & = & -24\end{array}

\implies \dfrac{35}{3}x=-24

Multiply both sides by 3:

\implies 35x=-72

Divide both sides by 35:

\implies x=-\dfrac{72}{35}

To find the y-value, substitute the found value of x into Equation 1 and solve for y:

\implies \dfrac{1}{8}\left(-\dfrac{72}{35}\right)-\dfrac{1}{2}y=1

\implies -\dfrac{72}{280}-1=\dfrac{1}{2}y

\implies -\dfrac{44}{35}=\dfrac{1}{2}y

\implies y=-\dfrac{88}{35}

<u>Solution</u>

\left(-\dfrac{72}{35},-\dfrac{88}{35}\right)

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