Solve by the substitution method.
2x+7y=16
x=22-7y
2x+7y=16
plug 22-7y for x
so
2(22-7y) + 7y=16
44-14y+7y=16
-7y= -44+16
-7y=-28
so y= 4
To solve the system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation.
Let's start with the second equation:
x = 22 - 7y
Now substitute this expression for x in the first equation:
2(22 - 7y) + 7y = 16
Now simplify and solve for y:
44 - 14y + 7y = 16
-7y = 16 - 44
-7y = -28
y = (-28) / (-7)
y = 4
Now substitute the value of y back into the second equation to solve for x:
x = 22 - 7y
x = 22 - 7(4)
x = 22 - 28
x = -6
So the solution to the system of equations is x = -6 and y = 4.