Answer:
[tex]\left(-\dfrac{72}{35},-\dfrac{88}{35}\right)[/tex]
Step-by-step explanation:
[tex]\textsf{Equation 1}: \quad \dfrac{1}{8}x-\dfrac{1}{2}y=1[/tex]
[tex]\textsf{Equation 2}: \quad \dfrac{1}{3}x+\dfrac{1}{8}y=-1[/tex]
Multiply Equation 1 by 8:
[tex]\textsf{Equation 1}: \quad 8\left(\dfrac{1}{8}x-\dfrac{1}{2}y=1\right)\implies x-4y=8[/tex]
Multiply Equation 2 by 32:
[tex]\textsf{Equation 2}: \quad 32\left(\dfrac{1}{3}x+\dfrac{1}{8}y=-1\right)\implies \dfrac{32}{3}x+4y=-32[/tex]
Add the new equations together to eliminate y:
[tex]\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}[/tex]
[tex]\implies \dfrac{35}{3}x=-24[/tex]
Multiply both sides by 3:
[tex]\implies 35x=-72[/tex]
Divide both sides by 35:
[tex]\implies x=-\dfrac{72}{35}[/tex]
To find the y-value, substitute the found value of x into Equation 1 and solve for y:
[tex]\implies \dfrac{1}{8}\left(-\dfrac{72}{35}\right)-\dfrac{1}{2}y=1[/tex]
[tex]\implies -\dfrac{72}{280}-1=\dfrac{1}{2}y[/tex]
[tex]\implies -\dfrac{44}{35}=\dfrac{1}{2}y[/tex]
[tex]\implies y=-\dfrac{88}{35}[/tex]
Solution
[tex]\left(-\dfrac{72}{35},-\dfrac{88}{35}\right)[/tex]
