Questions: Система 2x₁+2x₂=10 3x₁+2x₂=15

Transcript text: Система $\left\{\begin{array}{l}2 x_{1}+2 x_{2}=10 \\ 3 x_{1}+2 x_{2}=15\end{array}\right.$

Solution

Solution Steps

Step 1: Write down the system of equations

The given system of equations is: \[ \begin{cases} 2x_1 + 2x_2 = 10 \\ 3x_1 + 2x_2 = 15 \end{cases} \]

Step 2: Subtract the first equation from the second

Subtract the first equation from the second to eliminate $x_2$: \[ (3x_1 + 2x_2) - (2x_1 + 2x_2) = 15 - 10 \] Simplify: \[ x_1 = 5 \]

Step 3: Substitute $x_1 = 5$ into the first equation

Substitute $x_1 = 5$ into the first equation to solve for $x_2$: \[ 2(5) + 2x_2 = 10 \] Simplify: \[ 10 + 2x_2 = 10 \] Subtract 10 from both sides: \[ 2x_2 = 0 \] Divide by 2: \[ x_2 = 0 \]

Final Answer

The solution to the system is: \[ \boxed{x_1 = 5, \quad x_2 = 0} \]

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