Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 3. {1/2x + 1/3y = 2 {1/5x - 2/3y = 8

Answer 1

To solve the system of equations, multiply the first equation by 6 and the second by 15 to clear the fractions. Then, subtract equation 2 from equation 1 to solve for y. Finally, substitute the value of y back into equation 1 to solve for x.

Step-by-step explanation:

To solve the given system of equations:

1. Multiply the first equation by 6 and the second equation by 15 to clear the fractions:

• 3x + 2y = 12 (equation 1)
• 3x - 10y = 120 (equation 2)

2. Subtract equation 2 from equation 1:

• (3x + 2y) - (3x - 10y) = 12 - 120
• 12y = -108
• y = -9

3. Substitute the value of y back into equation 1 to solve for x:

• 3x + 2(-9) = 12
• 3x - 18 = 12
• 3x = 30
• x = 10

Therefore, the solution to the system of equations is x = 10 and y = -9. The solution is unique.