Let a be the number
Let b be the other number
[tex]\large \tt \red{given} \begin{cases} \sf \: 2a = b + 2 \: \: \: \tt \red{(eq.1)} \\ \sf \: a + b = 16 \: \: \: \tt \red{(eq.2)} \end{cases} \\ \\ [/tex]
Solve for the value of b. Use the second equation.
[tex] \sf \large\begin{align} \sf a + b &= \sf16 \\ \sf b &= \sf16 - a \end{align} [/tex]
[tex] \: [/tex]
Substitute the expression of b to the first equation to find the value of a
[tex]\sf \large\begin{align} \sf 2a &= \sf 16 - a + 2 \\ \sf 2a &= \sf 18 - a \\ \sf a + 2a &= \sf 18 \\ \sf 3a &= \sf 18 \\\sf \frac{ \cancel3a}{ \cancel3} &= \sf \frac{18}{3} \\ \sf \orange a & \orange{ = \sf 6} \end{align} [/tex]
[tex] \: [/tex]
Use the b equation to find the value of b. Substitute a as 6.
[tex]\sf \large\begin{align} \sf b &= \sf16 - 6 \\ \sf \orange b & \orange{= \sf10} \end{align} [/tex]
[tex] \: [/tex]
[tex] \large \implies \huge \sf \orange{6 \: and \: 10}[/tex]
#CarryOnLearning
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