solve using the subsitution method
4x+4y=36
4x+4y=12
If the system has no solution or an infinite number of solutions, please help me understand it.
Even without the substitution method, how can 4x+4y = both 12 and 36?
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 by solving the first equation, 4x + 4y = 36, for x:
4x + 4y = 36
Subtract 4y from both sides:
4x = 36 - 4y
Divide both sides by 4:
x = (36 - 4y) / 4
Simplify:
x = 9 - y
Now, we substitute this expression for x into the second equation and solve for y:
4x + 4y = 12
Replace x with 9 - y:
4(9 - y) + 4y = 12
Distribute:
36 - 4y + 4y = 12
Combine like terms:
36 = 12
Since this equation is not true, we have reached a contradiction. This means that the system of equations has no solution. Graphically, the two equations represent parallel lines that never intersect, indicating that there is no common solution.
In summary, the system of equations 4x + 4y = 36 and 4x + 4y = 12 has no solution.