Question

Determine the solutions to the system of equations.

x + 2y = -6
4x + 6y = -26
Option 1: No solutions
Option 2: Infinitely many solutions
Option 3: Exactly one solution
Option 4: Cannot be determined

Answer 1

To solve the system of equations x + 2y = -6 and 4x + 6y = -26, we can use the method of substitution. The solution is x = -8 and y = 1, which corresponds to exactly one solution.

Step-by-step explanation:

To determine the solutions to the system of equations x + 2y = -6 and 4x + 6y = -26, we can solve the system using the method of substitution or elimination. Let's use the method of substitution.

1. From the first equation, solve for x in terms of y: x = -6 - 2y.
2. Substitute the value of x into the second equation: 4(-6 - 2y) + 6y = -26.
3. Simplify and solve for y: -24 - 8y + 6y = -26.
4. Combine like terms: -24 - 2y = -26.
5. Add 24 to both sides: -2y = -2.
6. Divide by -2: y = 1.
7. Substitute the value of y back into the first equation to solve for x: x + 2(1) = -6.
8. Simplify and solve for x: x + 2 = -6.
9. Subtract 2 from both sides: x = -8.

Therefore, the solution to the system of equations is x = -8 and y = 1, which corresponds to exactly one solution.