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 {3x+2y=0 {-x- 2y=8

Answer 1

To solve the system of equations, we can use substitution method. The solution to the system of equations is (x, y) = (4, -6).

Step-by-step explanation:

To solve the system of equations, we can use the method of substitution or elimination. Let's use substitution:

1. From the first equation, solve for x in terms of y: x = -2y/3
2. Substitute this value of x into the second equation: -(-2y/3) - 2y = 8
3. Simplify and solve for y: 2y/3 - 2y = 8
4. Multiply both sides by 3 to eliminate the fraction: 2y - 6y = 24
5. Combine like terms: -4y = 24
6. Divide both sides by -4: y = -6
7. Substitute this value of y back into the first equation to solve for x: 3x + 2(-6) = 0
8. Simplify and solve for x: 3x - 12 = 0
9. Add 12 to both sides: 3x = 12
10. Divide both sides by 3: x = 4

The solution to the system of equations is (x, y) = (4, -6).