solve the following system by the substitution method 3x+4y=27 x=y+2
To solve the system by the substitution method, we first solve one of the equations for one variable and substitute it into the other equation.
From the second equation, we have x = y + 2.
Substituting this value of x into the first equation, we get:
3(y + 2) + 4y = 27.
Simplifying the equation gives:
3y + 6 + 4y = 27.
Combining like terms, we have:
7y + 6 = 27.
Subtracting 6 from both sides, we get:
7y = 21.
Dividing both sides by 7, we have:
y = 3.
Now substitute this value of y back into the second equation to find x:
x = y + 2 = 3 + 2 = 5.
Therefore, the solution to the system of equations is x = 5 and y = 3.