Question

1. solve the system using elimination.

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$$\begin{cases} 4x + 9y = 4 \\\\ 4x - 9y = 4 \\end{cases}$$

select the correct choice below and fill in any answer boxes in your choice.
\bigcirc a. the solution is \boxed{}. (type an ordered pair.)
\bigcirc b. there are infinitely many solutions.
\bigcirc c. there is no solution.

Explanation:

Step1: Eliminate \( y \) by adding equations

Add the two equations \( 4x + 9y = 4 \) and \( 4x - 9y = 4 \) together.
\( (4x + 9y) + (4x - 9y) = 4 + 4 \)
Simplify the left - hand side: \( 4x+4x + 9y-9y=8x \), and the right - hand side is \( 8 \). So we get \( 8x=8 \).

Step2: Solve for \( x \)

Divide both sides of the equation \( 8x = 8 \) by \( 8 \).
\( x=\frac{8}{8}=1 \)

Step3: Substitute \( x = 1 \) into one of the original equations to solve for \( y \)

Substitute \( x = 1 \) into the first equation \( 4x+9y = 4 \).
We have \( 4\times1+9y = 4 \), which simplifies to \( 4 + 9y=4 \).
Subtract \( 4 \) from both sides: \( 9y=4 - 4=0 \).
Divide both sides by \( 9 \): \( y = 0 \)

Answer:

A. The solution is \((1,0)\)