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Sagot :
To solve the system of equations:
[tex]\[ \begin{array}{l} 3x - 2y = 4 \\ x + y = 2 \end{array} \][/tex]
we will use the substitution or elimination method. Here, I'll demonstrate using the substitution method.
1. Solve the second equation for [tex]\( x \)[/tex]:
[tex]\[ x + y = 2 \implies x = 2 - y \][/tex]
2. Substitute [tex]\( x = 2 - y \)[/tex] into the first equation:
[tex]\[ 3(2 - y) - 2y = 4 \][/tex]
3. Simplify and solve for [tex]\( y \)[/tex]:
[tex]\[ 6 - 3y - 2y = 4 \\ 6 - 5y = 4 \\ -5y = 4 - 6 \\ -5y = -2 \\ y = \frac{2}{5} \][/tex]
4. Substitute [tex]\( y = \frac{2}{5} \)[/tex] back into the equation [tex]\( x = 2 - y \)[/tex]:
[tex]\[ x = 2 - \frac{2}{5} \\ x = \frac{10}{5} - \frac{2}{5} \\ x = \frac{8}{5} \][/tex]
Thus, the values are:
[tex]\[ x = \frac{8}{5}, \quad y = \frac{2}{5} \][/tex]
So, the correct choice is [tex]\( \boxed{D} \)[/tex].
[tex]\[ \begin{array}{l} 3x - 2y = 4 \\ x + y = 2 \end{array} \][/tex]
we will use the substitution or elimination method. Here, I'll demonstrate using the substitution method.
1. Solve the second equation for [tex]\( x \)[/tex]:
[tex]\[ x + y = 2 \implies x = 2 - y \][/tex]
2. Substitute [tex]\( x = 2 - y \)[/tex] into the first equation:
[tex]\[ 3(2 - y) - 2y = 4 \][/tex]
3. Simplify and solve for [tex]\( y \)[/tex]:
[tex]\[ 6 - 3y - 2y = 4 \\ 6 - 5y = 4 \\ -5y = 4 - 6 \\ -5y = -2 \\ y = \frac{2}{5} \][/tex]
4. Substitute [tex]\( y = \frac{2}{5} \)[/tex] back into the equation [tex]\( x = 2 - y \)[/tex]:
[tex]\[ x = 2 - \frac{2}{5} \\ x = \frac{10}{5} - \frac{2}{5} \\ x = \frac{8}{5} \][/tex]
Thus, the values are:
[tex]\[ x = \frac{8}{5}, \quad y = \frac{2}{5} \][/tex]
So, the correct choice is [tex]\( \boxed{D} \)[/tex].
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