solve using the substitution method. If the system has no solution or infinite number of solution state this
4x+4y=-36
4x+4y=12
4x + 4y = -36
-4x -4x
4y = -4x-36
/4 /4 /4
y = -x-9
Now you substitute this equation into the second one.
4x + 4(-x-9)= 12
Distribute the 4
4x-4x = -36
0x = -36
0 is not equal to -36, so that means this has no solution.
To solve the system of equations using the substitution method, we will isolate one variable in one of the equations and substitute it into the other equation. Let's solve the system of equations step-by-step:
Equation 1: 4x + 4y = -36
Equation 2: 4x + 4y = 12
Step 1: Solve Equation 1 for one variable.
Let's solve Equation 1 for x:
4x = -36 - 4y
Dividing both sides by 4:
x = (-36 - 4y)/4
x = -9 - y.
Step 2: Substitute the expression for x into Equation 2.
In Equation 2, substitute the expression for x:
4(-9 - y) + 4y = 12
Step 3: Simplify and solve for y.
-36 - 4y + 4y = 12
-36 = 12
Step 4: Analyze the result.
Since -36 does not equal 12, the equation -36 = 12 is false. Therefore, the system of equations has no solution.
Conclusion: The system of equations 4x + 4y = -36 and 4x + 4y = 12 has no solution.
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation.
Given:
Equation 1: 4x + 4y = -36
Equation 2: 4x + 4y = 12
Step 1: Solve one equation for one variable.
Let's solve Equation 1 for x:
4x + 4y = -36
We can rewrite this equation in terms of x:
4x = -36 - 4y
Divide both sides by 4:
x = (-36 - 4y) / 4
x = -9 - y
Step 2: Substitute the expression x = -9 - y into the other equation.
Substitute x = -9 - y into Equation 2:
4x + 4y = 12
4(-9 - y) + 4y = 12
-36 - 4y + 4y = 12
-36 = 12
Step 3: Simplify and evaluate.
We can see that -36 does not equal 12. Therefore, there is no solution to the system of equations.
Conclusion:
The system of equations has no solution.