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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].
[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].
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