x − 5y = 7 and 3x − 2y = −4

Answer 1

To solve the system of equations, we first want to eliminate one of the variables. I'll eliminate y using the addition method:

Given the two equations:
1) x - 5y = 7
2) 3x - 2y = -4

First, we can multiply the first equation by 2 and the second equation by 5 to make the coefficients in front of y the same:

1) 2(x - 5y) = 2(7) => 2x - 10y = 14
2) 5(3x - 2y) = 5(-4) => 15x - 10y = -20

Now we can add the two new equations together:
(2x - 10y) + (15x - 10y) = 14 + (-20)
17x = -6
Now, divide by 17 to isolate x:
x = -6/17

Now that we have the value for x, we can substitute it back into either of the original equations to find the value for y. I'll use the first equation:

(-6/17) - 5y = 7
Now, we want to get rid of the fractions, so multiply by 17:
-6 - 85y = 119
Now, we'll add 6 to both sides of the equation:
-85y = 125
Now, divide by -85 to isolate y:
y = 125/-85

So, the solution to the system of equations is x = -6/17, y = 125/-85.