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МатематикаВопрос:
Solve the system of equations: 3x + 4y - 11 = 0 5x - 2y - 14 = 0
Ответ:
System of Equations:
- Equation 1: 3x + 4y - 11 = 0
- Equation 2: 5x - 2y - 14 = 0
Brief Explanation: To solve this system, we can use either the substitution method or the elimination method. The elimination method seems more straightforward here if we multiply the second equation by 2 to eliminate 'y'.
Step-by-step solution:
- Step 1: Rewrite the equations in a standard form (Ax + By = C).
Equation 1: 3x + 4y = 11
Equation 2: 5x - 2y = 14 - Step 2: Multiply Equation 2 by 2 to make the coefficients of 'y' opposites.
2 * (5x - 2y) = 2 * 14
10x - 4y = 28 - Step 3: Add the modified Equation 2 to Equation 1.
(3x + 4y) + (10x - 4y) = 11 + 28
13x = 39 - Step 4: Solve for 'x'.
x = 39 / 13
x = 3 - Step 5: Substitute the value of 'x' (which is 3) into either of the original equations to solve for 'y'. Let's use Equation 1.
3(3) + 4y = 11
9 + 4y = 11 - Step 6: Solve for 'y'.
4y = 11 - 9
4y = 2
y = 2 / 4
y = 1/2
Answer: x = 3, y = 1/2
