Answer:
The solution is:
[tex](\frac{137}{13}, -\frac{152}{13})[/tex]
Step-by-step explanation:
We have the following equations
[tex]3x - 2y =55[/tex]
[tex]-2x - 3y = 14[/tex]
To solve the system multiply by [tex]\frac{3}{2}[/tex] the second equation and add it to the first equation
[tex]-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}[/tex]
[tex]-3x - \frac{9}{2}y = 21[/tex]
[tex]3x - 2y =55[/tex]
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[tex]-\frac{13}{2}y=76[/tex]
[tex]y=-76*\frac{2}{13}[/tex]
[tex]y=-\frac{152}{13}[/tex]
Now substitute the value of y in any of the two equations and solve for x
[tex]-2x - 3(-\frac{152}{13}) = 14[/tex]
[tex]-2x +\frac{456}{13} = 14[/tex]
[tex]-2x= 14-\frac{456}{13}[/tex]
[tex]-2x=-\frac{274}{13}[/tex]
[tex]x=\frac{137}{13}[/tex]
The solution is:
[tex](\frac{137}{13}, -\frac{152}{13})[/tex]
