Final answer:
To solve the system of equations, we can use the method of elimination. Multiply the equations by suitable numbers to eliminate the fractions, and then subtract one equation from the other to eliminate one variable. Solve for the remaining variable and substitute it back into an equation to find the value of the other variable.
Step-by-step explanation:
To find the solution to the system of equations, we need to solve them simultaneously. The given equations are:
y = (2/5)x - 3
y = (-4/5)x - 9
We can solve this system of equations by substitution or elimination. Let's use elimination to find the values of x and y.
Multiplying the first equation by 5 and the second equation by 5 to clear the fractions, we get:
5y = 2x - 15
5y = -4x - 45
Now we can subtract the second equation from the first equation to eliminate the y variable:
(5y - 5y) = (2x - 4x) - (15 + 45)
0 = -2x - 60
2x = -60
x = -30
Substituting the value of x into the first equation, we can solve for y:
y = (2/5)(-30) - 3
y = -12 - 3
y = -15
Therefore, the solution to the system of equations is (-30, -15).