Math  /  Algebra

Questionlist
Solve the system by the addition method 2x+4y=22x4y=2\begin{array}{l} 2 x+4 y=2 \\ 2 x-4 y=2 \end{array}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The sofution set is \{ . (Type an ordered pair) B. There are infinitely many solutions C. There is no solution e this View an example Get more help - Clear all Check answer Search 5:30 PM 11/28/2024

Studdy Solution

STEP 1

1. We are solving a system of linear equations using the addition method (also known as the elimination method).
2. The system of equations is: $ \begin{align*} 2x + 4y &= 2 \\ 2x - 4y &= 2 \end{align*} \]
3. The goal is to eliminate one of the variables by adding the equations together.

STEP 2

1. Align the equations for addition.
2. Add the equations to eliminate one of the variables.
3. Solve for the remaining variable.
4. Substitute the found value back into one of the original equations to find the other variable.
5. Determine the nature of the solution set.

STEP 3

Write the system of equations clearly:
\begin{align*} 2x + 4y &= 2 \\ 2x - 4y &= 2 \end{align*}

STEP 4

Add the two equations together to eliminate y y :
(2x+4y)+(2x4y)=2+2(2x + 4y) + (2x - 4y) = 2 + 2

STEP 5

Simplify the resulting equation:
4x=44x = 4

STEP 6

Solve for x x by dividing both sides by 4:
x=1x = 1

STEP 7

Substitute x=1 x = 1 back into one of the original equations to solve for y y . Using the first equation:
2(1)+4y=22(1) + 4y = 2
Simplify:
2+4y=22 + 4y = 2
Subtract 2 from both sides:
4y=04y = 0
Divide by 4:
y=0y = 0

STEP 8

The solution set is the ordered pair (1,0)(1, 0).
Therefore, the correct choice is:
A. The solution set is {(1,0)}\{ (1, 0) \}.

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