solve the following system by the substitution method 2x+7y=8 x-2y=4
To solve the system using the substitution method, we start with the second equation:
x - 2y = 4
We can solve for x in terms of y by isolating x:
x = 2y + 4
Now we substitute this expression for x in the first equation:
2(2y + 4) + 7y = 8
Distribute the 2:
4y + 8 + 7y = 8
Combine like terms:
11y + 8 = 8
Subtract 8 from both sides:
11y = 0
Divide both sides by 11:
y = 0
Now we substitute this value of y back into the second equation to solve for x:
x - 2(0) = 4
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 0.