Answer: Therefore, a reasonable estimate for the solution of the given equations is x ≈ -0.268 and y ≈ -0.304.
Explanation:
To find a reasonable estimate for the solution, we can use the method of substitution. Step 1: From equation (1), we can express y in terms of x: y = 3x + 1/2 Step 2: Substitute the value of y from equation (1) into equation (2): 3x + 1/2 = 1/5x - 1/4 Step 3: Simplify the equation: Multiply both sides of the equation by 20 to eliminate the fractions: 20(3x + 1/2) = 20(1/5x - 1/4) 60x + 10 = 4x - 5 Step 4: Simplify further: Combine like terms: 60x - 4x = -5 - 10 56x = -15 Step 5: Solve for x: Divide both sides of the equation by 56: x = -15/56 Step 6: Substitute the value of x back into equation (1) to find y: y = 3(-15/56) + 1/2 Step 7: Simplify further: Multiply 3 by -15/56: y = -45/56 + 1/2 Step 8: Simplify the equation: Find a common denominator for -45/56 and 1/2, which is 112: y = -45/56 + 56/112 y = -45/56 + 1/2 Step 9: Simplify further: Multiply -45/56 by 2/2: y = -90/112 + 56/112 y = -90/112 + 56/112 Step 10: Simplify the equation: Combine like terms: y = -34/112