Get detailed and reliable answers to your questions with IDNLearn.com. Join our Q&A platform to access reliable and detailed answers from experts in various fields.
Sagot :
To find the solution to the given system of equations:
[tex]\[ \begin{cases} 3x + 4y = -2 \\ 2x - 4y = -8 \end{cases} \][/tex]
we will solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Step 1: Write the equations
- The first equation is:
[tex]\[ 3x + 4y = -2 \][/tex]
- The second equation is:
[tex]\[ 2x - 4y = -8 \][/tex]
### Step 2: Add the equations to eliminate [tex]\( y \)[/tex]
If we add both equations together, we get:
[tex]\[ (3x + 4y) + (2x - 4y) = -2 + (-8) \][/tex]
This simplifies to:
[tex]\[ 3x + 2x + 4y - 4y = -10 \][/tex]
[tex]\[ 5x = -10 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Divide by 5:
[tex]\[ x = \frac{-10}{5} = -2 \][/tex]
### Step 4: Substitute [tex]\( x \)[/tex] back into one of the original equations
Let’s use the first equation:
[tex]\[ 3x + 4y = -2 \][/tex]
Substitute [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2) + 4y = -2 \][/tex]
This simplifies to:
[tex]\[ -6 + 4y = -2 \][/tex]
### Step 5: Solve for [tex]\( y \)[/tex]
Add 6 to both sides:
[tex]\[ 4y = -2 + 6 = 4 \][/tex]
Divide by 4:
[tex]\[ y = \frac{4}{4} = 1 \][/tex]
### Final Answer
The solution of the system of equations is:
[tex]\[ x = -2 \quad \text{and} \quad y = 1 \][/tex]
Thus, the correct answer is:
(D) [tex]\( x = -2, y = 1 \)[/tex].
[tex]\[ \begin{cases} 3x + 4y = -2 \\ 2x - 4y = -8 \end{cases} \][/tex]
we will solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Step 1: Write the equations
- The first equation is:
[tex]\[ 3x + 4y = -2 \][/tex]
- The second equation is:
[tex]\[ 2x - 4y = -8 \][/tex]
### Step 2: Add the equations to eliminate [tex]\( y \)[/tex]
If we add both equations together, we get:
[tex]\[ (3x + 4y) + (2x - 4y) = -2 + (-8) \][/tex]
This simplifies to:
[tex]\[ 3x + 2x + 4y - 4y = -10 \][/tex]
[tex]\[ 5x = -10 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Divide by 5:
[tex]\[ x = \frac{-10}{5} = -2 \][/tex]
### Step 4: Substitute [tex]\( x \)[/tex] back into one of the original equations
Let’s use the first equation:
[tex]\[ 3x + 4y = -2 \][/tex]
Substitute [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2) + 4y = -2 \][/tex]
This simplifies to:
[tex]\[ -6 + 4y = -2 \][/tex]
### Step 5: Solve for [tex]\( y \)[/tex]
Add 6 to both sides:
[tex]\[ 4y = -2 + 6 = 4 \][/tex]
Divide by 4:
[tex]\[ y = \frac{4}{4} = 1 \][/tex]
### Final Answer
The solution of the system of equations is:
[tex]\[ x = -2 \quad \text{and} \quad y = 1 \][/tex]
Thus, the correct answer is:
(D) [tex]\( x = -2, y = 1 \)[/tex].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.