Answer :
To solve the system of equations using the elimination method, we first need to align the given equations as follows:
[tex]\[ \begin{cases} 8x - 5y = 5 \quad \quad (1)\\ -8x - 6y = 6 \quad (2) \end{cases} \][/tex]
Step 1: Add the equations.
Add equation (1) and equation (2) to eliminate [tex]\(x\)[/tex]:
[tex]\[ (8x - 5y) + (-8x - 6y) = 5 + 6 \][/tex]
Simplify the left-hand side and the right-hand side:
[tex]\[ 8x - 8x - 5y - 6y = 5 + 6 \][/tex]
This simplifies to:
[tex]\[ -11y = 11 \][/tex]
Step 2: Solve for [tex]\(y\)[/tex].
Solve the simplified equation for [tex]\(y\)[/tex]:
[tex]\[ -11y = 11 \][/tex]
Divide both sides by [tex]\(-11\)[/tex]:
[tex]\[ y = -1 \][/tex]
Step 3: Substitute [tex]\(y\)[/tex] back into one of the original equations to solve for [tex]\(x\)[/tex].
Substitute [tex]\(y = -1\)[/tex] into equation (1):
[tex]\[ 8x - 5(-1) = 5 \][/tex]
Simplify the equation:
[tex]\[ 8x + 5 = 5 \][/tex]
Subtract 5 from both sides:
[tex]\[ 8x = 0 \][/tex]
Divide both sides by 8:
[tex]\[ x = 0 \][/tex]
Step 4: Verify the solution.
Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = -1\)[/tex] back into both original equations to ensure they hold true.
For the first equation:
[tex]\[ 8(0) - 5(-1) = 5 \][/tex]
Simplifies to:
[tex]\[ 0 + 5 = 5 \][/tex]
Which is true. For the second equation:
[tex]\[ -8(0) - 6(-1) = 6 \][/tex]
Simplifies to:
[tex]\[ 0 + 6 = 6 \][/tex]
Which is also true.
Thus, the solution to the system is:
[tex]\[ (x, y) = (0, -1) \][/tex]
So, the correct answer is:
[tex]\[ \boxed{(0, -1)} \][/tex]
[tex]\[ \begin{cases} 8x - 5y = 5 \quad \quad (1)\\ -8x - 6y = 6 \quad (2) \end{cases} \][/tex]
Step 1: Add the equations.
Add equation (1) and equation (2) to eliminate [tex]\(x\)[/tex]:
[tex]\[ (8x - 5y) + (-8x - 6y) = 5 + 6 \][/tex]
Simplify the left-hand side and the right-hand side:
[tex]\[ 8x - 8x - 5y - 6y = 5 + 6 \][/tex]
This simplifies to:
[tex]\[ -11y = 11 \][/tex]
Step 2: Solve for [tex]\(y\)[/tex].
Solve the simplified equation for [tex]\(y\)[/tex]:
[tex]\[ -11y = 11 \][/tex]
Divide both sides by [tex]\(-11\)[/tex]:
[tex]\[ y = -1 \][/tex]
Step 3: Substitute [tex]\(y\)[/tex] back into one of the original equations to solve for [tex]\(x\)[/tex].
Substitute [tex]\(y = -1\)[/tex] into equation (1):
[tex]\[ 8x - 5(-1) = 5 \][/tex]
Simplify the equation:
[tex]\[ 8x + 5 = 5 \][/tex]
Subtract 5 from both sides:
[tex]\[ 8x = 0 \][/tex]
Divide both sides by 8:
[tex]\[ x = 0 \][/tex]
Step 4: Verify the solution.
Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = -1\)[/tex] back into both original equations to ensure they hold true.
For the first equation:
[tex]\[ 8(0) - 5(-1) = 5 \][/tex]
Simplifies to:
[tex]\[ 0 + 5 = 5 \][/tex]
Which is true. For the second equation:
[tex]\[ -8(0) - 6(-1) = 6 \][/tex]
Simplifies to:
[tex]\[ 0 + 6 = 6 \][/tex]
Which is also true.
Thus, the solution to the system is:
[tex]\[ (x, y) = (0, -1) \][/tex]
So, the correct answer is:
[tex]\[ \boxed{(0, -1)} \][/tex]
Answer:
D. (0, -1)
Step-by-step explanation:
Pre-Solving
We are given the following system of equations:
8x - 5y = 5
-8x - 6y = 6
We want to solve it using elimination. We will add the equations together in order to clear one of the variables, then solve for the other variable.
Solving
First, add the equations together.
8x - 5y = 5
-8x - 6y = 6
___________________
-11y = 11
Divide both sides by -11.
y = -1
Now, substitute -1 as y into either 8x - 5y = 5 or -8x - 6y = 6.
8x - 5(-1) = 5
8x + 5 = 5
8x = 0
x = 0
So, the answer is (0, -1), which is D.
