For the following system of equations, what is the x-value of the solution?
-x + 2y = 6
6y = x + 18
A. -18
B. 0
C. -6
D. 3
Confused? Still trying to work it out. Please help! Thanks
Is it 0?
first line them up properly
#1: -x + 2y = 6
#2: x - 6y = -18
add them:
-4y = -12
y = 3
in #1:
-x + 6 = 6
-x = 0
x = 0
why did you not sub your values back in to see if you are correct ?
To find the x-value of the solution for the given system of equations, we can solve the equations simultaneously using the method of substitution. Let's start by solving one of the equations for x.
From the first equation, we have:
-x + 2y = 6
Rearranging the equation, we get:
x = 2y - 6
Now, we substitute this value of x into the second equation:
6y = x + 18
6y = (2y - 6) + 18
Simplifying, we have:
6y = 2y + 12
Now, let's isolate the variable y:
6y - 2y = 2y + 12 - 2y
4y = 12
Dividing both sides of the equation by 4, we find:
y = 12/4
Simplifying, we get:
y = 3
Now, we substitute this value of y back into the equation we found for x:
x = 2y - 6
x = 2(3) - 6
x = 6 - 6
x = 0
Therefore, the x-value of the solution for the given system of equations is 0. The correct answer is B.
To find the x-value of the solution, we need to solve the given system of equations. Let's go step-by-step:
Step 1: Solve one equation for one variable in terms of the other variable.
I will solve the first equation for x:
-x + 2y = 6
-x = -2y + 6
x = 2y - 6
Step 2: Substitute the expression for x in the other equation.
Now, replace x in the second equation with 2y - 6:
6y = (2y - 6) + 18
Step 3: Simplify and solve for y.
Let's simplify the equation:
6y = 2y + 12
Subtract 2y from both sides:
6y - 2y = 2y + 12 - 2y
4y = 12
Divide both sides by 4:
4y/4 = 12/4
y = 3
Step 4: Substitute the obtained value of y back into one of the original equations to solve for x.
Using the first equation:
-x + 2y = 6
-x + 2(3) = 6
-x + 6 = 6
-x = 0
x = 0
So, the solution to the system of equations is x = 0, y = 3.
Therefore, the x-value of the solution is B. 0.