What is the answer to 7x+2y=16 and -21x-6y=24 using the substituion method?
There's either a typo, or it's a trick question. Take a look at the equations.
7x+2y=16
-21x-6y=24
If you divide the 2nd by -3, you get
7x+2y = -8
There is no solution, since the left sides are the same, but the right is different. The lines are parallel.
To solve the system of equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation. Let's solve the first equation for x:
7x + 2y = 16
Rearranging the equation, we get:
7x = 16 - 2y
Dividing both sides by 7, we have:
x = (16 - 2y) / 7
Now, substitute this expression for x into the second equation:
-21x - 6y = 24
Replacing x, we get:
-21((16 - 2y) / 7) - 6y = 24
Expanding, we have:
-3(16 - 2y) - 6y = 24
Now, simplify:
-48 + 6y - 6y = 24
-48 = 24
This equation is not true, and there is no solution for this system of equations. The system of equations is inconsistent.
To solve the system of equations using the substitution method, we will express one variable in terms of the other and substitute it into the other equation. Let's solve the system:
Equation 1: 7x + 2y = 16
Equation 2: -21x - 6y = 24
Step 1: Solve Equation 1 for one variable in terms of the other. Let's solve Equation 1 for x:
7x + 2y = 16
7x = 16 - 2y
x = (16 - 2y) / 7
Step 2: Substitute the expression for x into Equation 2 and solve for y:
-21x - 6y = 24
-21((16 - 2y) / 7) - 6y = 24 (Substituting x from Equation 1)
-3(16 - 2y) - 6y = 24 (Simplifying the fraction)
-48 + 6y - 6y = 24 (Distribute -3)
-48 = 24 (Combining like terms)
Step 3: Determine if the equation is true or false. Since the equation is false (-48 = 24), this means there is no solution to the system of equations. The two equations represent parallel lines that do not intersect.
Therefore, the system of equations has no solution.