To solve the system of equations:
Equation 1: -5x + 2y = 9
Equation 2: y = 7x
We can substitute the value of y from Equation 2 into Equation 1 to eliminate y and solve for x:
-5x + 2(7x) = 9
-5x + 14x = 9
9x = 9
x = 1
Now that we have the value of x, we can substitute it back into Equation 2 to find y:
y = 7(1)
y = 7
Therefore, the solution to the system of equations is x = 1 and y = 7.