Lcm to eliminate y

Identify the least common multiple that would eliminate the y-variable.

6x - 5y = -4
4x + 2y = 28

Correct result:

l =  10
x =  4.125
y =  5.75

Solution:

$$\begin{gathered} 5\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ 2\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ LCM(5,2)=2\cdot 5=10 \\ l=LCM(5,2)=10 \end{gathered}$$

$$\begin{gathered} 6x-5y=-4 \\ 4x+2y=28 \\ 12x-10y=-8 \\ 20x+10y=28\cdot 5 \\ 32x+0=-8+28\cdot 5 \\ 32\cdot x+0=-8+28\cdot 5 \\ 32x=132 \\ x={\displaystyle \frac{33}{8}}=4.125 \end{gathered}$$

$$\begin{gathered} 6x-5y=-4 \\ 6\cdot 4.125-5y=-4 \\ 6\cdot 4.125-5\cdot y=-4 \\ 5y=28.75 \\ y={\displaystyle \frac{23}{4}}=5.75 \end{gathered}$$

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