Answer :

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]

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