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МатематикаВопрос:
Solve the system of equations using the algebraic method: -3x + 7y = 29 6x + 5y = 13
Ответ:
System of Equations:
- -3x + 7y = 29
- 6x + 5y = 13
Brief explanation: To solve this system of linear equations using the algebraic method (elimination or substitution), we aim to eliminate one variable by manipulating the equations. We will use the elimination method here.
Step-by-step solution:
- Step 1: Multiply the first equation by 2 to make the coefficients of 'x' opposites. This gives us:
-6x + 14y = 58 - Step 2: Add the modified first equation to the second equation:
(-6x + 14y) + (6x + 5y) = 58 + 13
19y = 71 - Step 3: Solve for 'y':
\( y = \frac{71}{19} \) - Step 4: Substitute the value of 'y' into the first original equation:
-3x + 7 * (\(\frac{71}{19}\)) = 29
-3x + \(\frac{497}{19}\) = 29 - Step 5: Solve for 'x':
-3x = 29 - \(\frac{497}{19}\)
-3x = \(\frac{29 \cdot 19 - 497}{19}\)
-3x = \(\frac{551 - 497}{19}\)
-3x = \(\frac{54}{19}\)
\( x = \frac{54}{19 \cdot (-3)} \)
\( x = \frac{-18}{19} \)
Answer: x = -18/19, y = 71/19
