Question

-8x +4y =12

3x + y = -7
Solve and what is the answer
a) Consistent
b) Inconsistent or dependent

Answer 1

The system of equations is solved using the elimination method, yielding a unique solution (x=-2, y=-1), and is therefore consistent, not inconsistent or dependent.

Step-by-step explanation:

To solve the system of linear equations given by:

• -8x + 4y = 12
• 3x + y = -7

We can employ the method of substitution or elimination. To use elimination, we can multiply the second equation by -4 to cancel out the y terms:

1. Multiplying the second equation by -4: -4(3x + y) = -4(-7)
2. We get: -12x - 4y = 28
3. Now adding this to the first equation: (-12x - 4y) + (-8x + 4y) = 28 + 12
4. Which simplifies to: -20x = 40
5. Dividing by -20, we find: x = -2
6. Substituting x into the second original equation: 3x + y = -7, gives us 3(-2) + y = -7.
7. Thus y = -7 + 6 = -1.

Therefore, the solution is x = -2 and y = -1. This system is consistent since it has a unique solution. It is neither inconsistent nor dependent.