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Math  /  Algebra

QuestionQuestion 4 of 10
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 6x+4y=32−6x+4y=8\begin{array}{l} 6 x+4 y=32 \\ -6 x+4 y=8 \end{array} A. (1,5)(1,5) B. (4,2)(4,2) C. (2,5)(2,5) D. (0,8)(0,8)

Studdy Solution

STEP 1

1. We are given a system of linear equations: $ \begin{array}{l} 6x + 4y = 32 \\ -6x + 4y = 8 \end{array} \]
2. We will use the elimination method to solve for the ordered pair \((x, y)\).
3. The elimination method involves adding or subtracting equations to eliminate one of the variables.

STEP 2

1. Align the equations for elimination.
2. Eliminate one variable by adding the equations.
3. Solve for the remaining variable.
4. Substitute back to find the other variable.
5. Check the solution with the given options.

STEP 3

Write the system of equations as given: 6x+4y=32−6x+4y=8\begin{array}{l} 6x + 4y = 32 \\ -6x + 4y = 8 \end{array}
Notice that the coefficients of xx are opposites, which is ideal for elimination.

STEP 4

Add the two equations together to eliminate xx:
(6x+4y)+(−6x+4y)=32+8(6x + 4y) + (-6x + 4y) = 32 + 8
This simplifies to:
0x+8y=400x + 8y = 40

STEP 5

Simplify the equation:
8y=408y = 40
Divide both sides by 8 to solve for yy:
y=408=5y = \frac{40}{8} = 5

STEP 6

Substitute y=5y = 5 back into one of the original equations to solve for xx. Let's use the first equation:
6x+4(5)=326x + 4(5) = 32
Simplify:
6x+20=326x + 20 = 32
Subtract 20 from both sides:
6x=126x = 12
Divide by 6:
x=126=2x = \frac{12}{6} = 2

STEP 7

The solution to the system is (x,y)=(2,5)(x, y) = (2, 5).
Check the solution against the given options:
A. (1,5)(1, 5) B. (4,2)(4, 2) C. (2,5)(2, 5) D. (0,8)(0, 8)
The correct ordered pair is (2,5)(2, 5), which matches option C.

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