Certainly! Let's solve the given system of equations step-by-step.
The system of equations is:
[tex]\[
\left\{\begin{array}{ll}
(1) & 2x - y = 6 \\
(2) & 4x + 2y = 3
\end{array}\right.
\][/tex]
### Step 1: Express one of the variables in terms of the other from one of the equations.
Let's take the first equation and solve for [tex]\( y \)[/tex]:
[tex]\[
2x - y = 6 \implies y = 2x - 6
\][/tex]
### Step 2: Substitute this expression into the other equation.
Now, substitute [tex]\( y = 2x - 6 \)[/tex] into the second equation:
[tex]\[
4x + 2(2x - 6) = 3
\][/tex]
### Step 3: Solve the resulting equation for [tex]\( x \)[/tex].
Expand and simplify the equation:
[tex]\[
4x + 4x - 12 = 3 \\
8x - 12 = 3 \\
8x = 3 + 12 \\
8x = 15 \\
x = \frac{15}{8}
\][/tex]
### Step 4: Substitute the value of [tex]\( x \)[/tex] back into the equation from step 1 to find [tex]\( y \)[/tex].
Substitute [tex]\( x = \frac{15}{8} \)[/tex] into [tex]\( y = 2x - 6 \)[/tex]:
[tex]\[
y = 2\left(\frac{15}{8}\right) - 6 \\
y = \frac{30}{8} - 6 \\
y = \frac{30}{8} - \frac{48}{8} \\
y = \frac{30 - 48}{8} \\
y = \frac{-18}{8} \\
y = -\frac{9}{4}
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
\left( x, y \right) = \left( \frac{15}{8}, -\frac{9}{4} \right)
\][/tex]
So the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are [tex]\( \frac{15}{8} \)[/tex] and [tex]\( -\frac{9}{4} \)[/tex] respectively.
