Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

1. Solve the following system of equations:

[tex]\[
\begin{cases}
3x - 4y = -6 \\
2x + 4y = 16
\end{cases}
\][/tex]


Sagot :

To solve the system of equations:
[tex]\[ \begin{cases} 3x - 4y = -6 \\ 2x + 4y = 16 \end{cases} \][/tex]

we can use the method of elimination to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

### Step-by-Step Solution

1. Add the equations to eliminate [tex]\( y \)[/tex]:
[tex]\[ 3x - 4y = -6 \][/tex]
[tex]\[ 2x + 4y = 16 \][/tex]

If we add these two equations together, the [tex]\( y \)[/tex]-terms will cancel out:
[tex]\[ (3x - 4y) + (2x + 4y) = -6 + 16 \\ 3x + 2x - 4y + 4y = -6 + 16 \\ 5x = 10 \][/tex]

2. Solve for [tex]\( x \)[/tex]:
[tex]\[ 5x = 10 \\ x = \frac{10}{5} \\ x = 2 \][/tex]

3. Substitute [tex]\( x = 2 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]:
Let's use the second equation:
[tex]\[ 2x + 4y = 16 \][/tex]

Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ 2(2) + 4y = 16 \\ 4 + 4y = 16 \][/tex]

4. Solve for [tex]\( y \)[/tex]:
[tex]\[ 4 + 4y = 16 \\ 4y = 16 - 4 \\ 4y = 12 \\ y = \frac{12}{4} \\ y = 3 \][/tex]

### Solution
The solution to the system of equations is:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 3 \][/tex]

Thus, the solution is [tex]\((2, 3)\)[/tex].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.