solve the system of equations: 5x+2y=14 , x-6y=22
To solve this system of equations, we can use the elimination method.
First, we will rewrite the equations in standard form:
5x + 2y = 14 ... (1)
x - 6y = 22 ... (2)
Next, we will multiply equation (2) by 5 in order to get the coefficients of x to be the same in both equations:
5(x - 6y) = 5(22)
5x - 30y = 110
Now we will rewrite the new equation:
5x - 30y = 110 ... (3)
5x + 2y = 14 ... (1)
Now we will subtract equation (1) from equation (3) in order to eliminate x:
(5x - 30y) - (5x + 2y) = 110 - 14
-32y = 96
Now we can solve for y:
y = -3
Now that we have found the value of y, we can substitute it back into either equation (1) or (2) to solve for x.
Let's substitute y = -3 into equation (1):
5x + 2(-3) = 14
5x - 6 = 14
5x = 20
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -3.