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МатематикаВопрос:
Solve the system of equations: {2x+y=30 (x-2y=5
Ответ:
System of Equations:
- Equation 1: 2x + y = 30
- Equation 2: x - 2y = 5
Brief explanation: We will solve this system using the substitution method. We'll express one variable in terms of the other from one equation and substitute it into the second equation.
Step-by-step solution:
- Step 1: Express y from Equation 1.
From 2x + y = 30, we get y = 30 - 2x. - Step 2: Substitute y into Equation 2.
Substitute (30 - 2x) for y in the second equation:
\[ x - 2(30 - 2x) = 5 \] - Step 3: Solve for x.
Distribute the -2:
\[ x - 60 + 4x = 5 \]
Combine like terms:
\[ 5x - 60 = 5 \]
Add 60 to both sides:
\[ 5x = 65 \]
Divide by 5:
\[ x = 13 \] - Step 4: Substitute the value of x back into the expression for y.
\[ y = 30 - 2x \]
\[ y = 30 - 2(13) \]
\[ y = 30 - 26 \]
\[ y = 4 \]
Answer: x = 13, y = 4
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