Respuesta :

BenjaminG123
Greetings!

Find the Solution/Point of Intersection:
[tex] \left \{ {{3x-2y=25} \atop {5y=2x-24}} \right. [/tex]

Rearrange the System:
[tex] \left \{ {{3x-2y=25} \atop {-2x+5y=-24}} \right. [/tex]

Multiply the First Equation by 2 and the Second Equation by 3:
[tex] \left \{ {{2(3x-2y)=2(25)} \atop {3(-2x+5y)=3(-24)}} \right. [/tex]

[tex] \left \{ {{6x-4y=50} \atop {-6x+15y=-72}} \right. [/tex]

Eliminate the x variable:
[tex]+ \frac{\left \{ {{6x-4y=50} \atop {-6x+15y=-72}} \right. }{0x+11y=-22} [/tex]

[tex]11y=-22[/tex]

Divide both sides by 11:
[tex] \frac{11y}{11}= \frac{-22}{11} [/tex]

[tex]y=-2[/tex]

Input this value into the First Equation: 
[tex]3x-2y=25[/tex]

[tex]3x-2(-2)=25[/tex]

Simplify:
[tex]3x+4=25[/tex]

[tex]3x=21[/tex]

Divide both sides by 3:
[tex] \frac{3x}{3} = \frac{21}{3} [/tex]

[tex]x=7[/tex]

The Solution/Point of Intersection is:
[tex]\boxed{(7,-2)}[/tex]

I hope this helped!
-Benjamin

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