Question

Solve the system of linear equations. Give your solution as an ordered pair, either as a fraction or a decimal with at least 3 decimal places.
1/8x - 1/2y = 1
1/3x + 1/8y = -1

Answer 1

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:

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

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

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

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

Solution

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