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МатематикаВопрос:
Solve the system of equations: { x - 5y = 4, 3x - 8y = -2.
Ответ:
System of Equations:
- Equation 1: \( x - 5y = 4 \)
- Equation 2: \( 3x - 8y = -2 \)
Logic: We will solve this system of linear equations using the substitution method. First, we will express 'x' from the first equation and then substitute it into the second equation to solve for 'y'. Finally, we will substitute the value of 'y' back into the first equation to find 'x'.
Step-by-step solution:
- Step 1: Express x from Equation 1.
From \( x - 5y = 4 \), we get \( x = 4 + 5y \). - Step 2: Substitute x into Equation 2.
Substitute \( x = 4 + 5y \) into \( 3x - 8y = -2 \):
\( 3(4 + 5y) - 8y = -2 \) - Step 3: Solve for y.
Distribute the 3: \( 12 + 15y - 8y = -2 \)
Combine like terms: \( 12 + 7y = -2 \)
Subtract 12 from both sides: \( 7y = -2 - 12 \)
\( 7y = -14 \)
Divide by 7: \( y = -2 \) - Step 4: Substitute y back into the expression for x.
Using \( x = 4 + 5y \) and \( y = -2 \):
\( x = 4 + 5(-2) \)
\( x = 4 - 10 \)
\( x = -6 \)
Answer: x = -6, y = -2
