Find the Intersection of the Inequalities y+5x=0 , 3x-2y=6

Problem

{[y+5*x=0],[3*x−2*y=6])

Solution

1. Solve the first equation for y to use the substitution method.

y=−5*x

2. Substitute the expression for y into the second equation.

3*x−2*(−5*x)=6

3. Simplify the equation by performing the multiplication.

3*x+10*x=6

4. Combine like terms to isolate the variable x

13*x=6

5. Divide both sides by 13 to find the value of x

x=6/13

6. Substitute the value of x back into the expression for y

y=−5*(6/13)

7. Calculate the final value for y

y=−30/13

Final Answer

(x,y)=(6/13,−30/13)

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