Answer:
(-10, -8)
Step-by-step explanation:
We are find the solution to the system of equations:
\(\begin{cases}2x-3y=4\\ 9x-8y=-26\end{cases}\)
In other words, we are finding the point at which the lines intersect: when their x- and y-values are equal.
We can find the x- and y-coordinates of the solution using the substitution method. First, we can solve for x in terms of y in the top equation:
\(2x-3y=4\)
\(2x=4+3y\)
\(x=\dfrac{4+3y}{2}\)
Next, we can substitute this definition for x into the bottom equation:
\(9x-8y=-26\)
\(9\!\left(\dfrac{4+3y}{2}\right) -8y = -26\)
\(\dfrac{9}{2}(4+3y)-8y=-26\)
\(18+\dfrac{27}{2}y - 8y = -26\)
\(18+\dfrac{27}{2}y - \dfrac{16}{2}y = -26\)
\(18+\dfrac{11}{2}y=-26\)
\(\dfrac{11}{2}y=-26 - 18\)
\(\dfrac{2}{11}\cdot\left(\dfrac{11}{2}y\right)=(-44)\cdot\dfrac{2}{11}\)
\(\boxed{y = -8}\)
Then, we can plug this y-value into the first equation to solve for x:
\(2x-3y=4\)
\(2x-3(-8)=4\)
\(2x - (-24)=4\)
\(2x+24=-4\)
\(2x=-20\)
\(\boxed{x=-10}\)
So, the solution to the system of equations is:
\(\huge\boxed{(-10, -8)}\)
