Answer:
(-10, -8)
Step-by-step explanation:
We are find the solution to the system of equations:
[tex]\begin{cases}2x-3y=4\\ 9x-8y=-26\end{cases}[/tex]
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:
[tex]2x-3y=4[/tex]
[tex]2x=4+3y[/tex]
[tex]x=\dfrac{4+3y}{2}[/tex]
Next, we can substitute this definition for x into the bottom equation:
[tex]9x-8y=-26[/tex]
[tex]9\!\left(\dfrac{4+3y}{2}\right) -8y = -26[/tex]
[tex]\dfrac{9}{2}(4+3y)-8y=-26[/tex]
[tex]18+\dfrac{27}{2}y - 8y = -26[/tex]
[tex]18+\dfrac{27}{2}y - \dfrac{16}{2}y = -26[/tex]
[tex]18+\dfrac{11}{2}y=-26[/tex]
[tex]\dfrac{11}{2}y=-26 - 18[/tex]
[tex]\dfrac{2}{11}\cdot\left(\dfrac{11}{2}y\right)=(-44)\cdot\dfrac{2}{11}[/tex]
[tex]\boxed{y = -8}[/tex]
Then, we can plug this y-value into the first equation to solve for x:
[tex]2x-3y=4[/tex]
[tex]2x-3(-8)=4[/tex]
[tex]2x - (-24)=4[/tex]
[tex]2x+24=-4[/tex]
[tex]2x=-20[/tex]
[tex]\boxed{x=-10}[/tex]
So, the solution to the system of equations is:
[tex]\huge\boxed{(-10, -8)}[/tex]
