Solve by Substitution 6x-4y=30 , 12x+5y=-18

Problem

{[6*x−4*y=30],[12*x+5*y=−18])

Solution

1. Isolate a variable in the first equation. We will solve for x in 6*x−4*y=30

6*x=4*y+30

x=(4*y+30)/6

x=2/3*y+5

2. Substitute the expression for x into the second equation, 12*x+5*y=−18

12*(2/3*y+5)+5*y=−18

3. Distribute the constant and simplify the equation.

8*y+60+5*y=−18

13*y+60=−18

4. Solve for y by isolating the variable.

13*y=−78

y=−6

5. Substitute the value of y back into the expression for x to find the value of x

x=2/3*(−6)+5

x=−4+5

x=1

Final Answer

(x,y)=(1,−6)

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