Solve the system of equations:

[tex]\[
\left\{\begin{array}{l}
3x - 2y = 5 \\
2x + 4y = 14
\end{array}\right.
\][/tex]



Answer :

Let's solve the system of equations step by step:

[tex]\[ \begin{cases} 3x - 2y = 5 \\ 2x + 4y = 14 \end{cases} \][/tex]

### Step 1: Solve one equation for one of the variables

Let's solve the first equation for \( x \):

[tex]\[ 3x - 2y = 5 \][/tex]

Add \( 2y \) to both sides:

[tex]\[ 3x = 5 + 2y \][/tex]

Divide both sides by 3:

[tex]\[ x = \frac{5 + 2y}{3} \][/tex]

### Step 2: Substitute into the other equation

Substitute \( x = \frac{5 + 2y}{3} \) into the second equation \( 2x + 4y = 14 \):

[tex]\[ 2\left(\frac{5 + 2y}{3}\right) + 4y = 14 \][/tex]

Multiply through by 3 to clear the fraction:

[tex]\[ 2(5 + 2y) + 12y = 42 \][/tex]

Distribute \( 2 \):

[tex]\[ 10 + 4y + 12y = 42 \][/tex]

Combine like terms:

[tex]\[ 10 + 16y = 42 \][/tex]

Subtract 10 from both sides:

[tex]\[ 16y = 32 \][/tex]

Divide by 16:

[tex]\[ y = 2 \][/tex]

### Step 3: Substitute back to find \( x \)

Substitute \( y = 2 \) back into the equation \( x = \frac{5 + 2y}{3} \):

[tex]\[ x = \frac{5 + 2(2)}{3} \][/tex]

Simplify:

[tex]\[ x = \frac{5 + 4}{3} = \frac{9}{3} = 3 \][/tex]

### Final Solution

The solution to the system of equations is:

[tex]\[ x = 3, \quad y = 2 \][/tex]

Therefore, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations are [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex].