Question

What is the solution for the two algebraic equations below

Answer 1

Greetings!

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

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

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

$\left \{ {{6x-4y=50} \atop {-6x+15y=-72}} \right.$

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

$11y=-22$

Divide both sides by 11:
$\frac{11y}{11}= \frac{-22}{11}$

$y=-2$

Input this value into the First Equation: 
$3x-2y=25$

$3x-2(-2)=25$

Simplify:
$3x+4=25$

$3x=21$

Divide both sides by 3:
$\frac{3x}{3} = \frac{21}{3}$

$x=7$

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

I hope this helped!
-Benjamin