Final answer:
The two given equations are dependent and represent the same line, so there isn't a unique solution. Using Gaussian elimination reveals that there are an infinite number of solutions for y and z that satisfy the equation y + z = 1.
Step-by-step explanation:
You've been given two equations to solve using Gaussian elimination:
- -4y - 4z = -4
- 12y + 12z = 12
To begin, we can simplify both equations by dividing them by -4 and 12, respectively, to get standard form:
As we observe, both equations are actually the same, or in other words, one is a multiple of the other. In this case, using Gaussian elimination won't yield a unique solution because the system of equations is dependent. The equations represent the same line, therefore, there are an infinite number of solutions along this line where y and z could be any value that satisfies the equation y + z = 1.