Find the solution of the system of equations 5x=-2+7y x-7y=-34

(1) 5x=-2+7y

(2) x-7y=-34

Using the method of substitution:

Isolating x from the equation (2):

(2) x-7y=-34

x-7y+7y=-34+7y

x=7y-34 (3)

Replacing x by 7y-34 in the first equation:

(1) 5x=-2+7y

5 (7y-34) = - 2+7y

Solving for y:

35y-170=-2+7y

35y-170+170-7y=-2+7y+170-7y

28y=168

28y/28=168/28

y=6

Replacing y by 6 in equation (3)

(3) x=7y-34

x=7 (6) - 34

x=42-34

x=8

Answer: The solution of the system of equations is: x=8 and y=6