Answer
(2, -1)
If the right-hand side changes to (4, 44), the new solution is (8, -4)
Work Step by Step
Take the triangular system of equations we found in problem 1:
2x+3y=1
-6y=6
Solve using back-substitution.
We can solve equation 2 using basic algebra;
-6y=6
6y=-6
y=-1
Now that we know the value of y, we can substitute y=-1 into equation 1 and solve for x
2x+3(-1)=1
2x-3=1
2x=4
x=2
Therefore, the solution to the equation is (2, -1)
However, the problem also asks for the new solution if the right-hand side of the equation changes to (4, 44) (The textbook is referring back to the original system, not the triangular system we created in problem one)
This creates a new system:
2x+3y=4
10x+9y=44
We can solve this new system using Gaussian Elimination. Multiply equation one by 5, and subtract equation one from equation 2
{10x+9y=44}-{10x+15y=20}={0x-6y=24}
Our new system of equations is:
2x+3y=4
-6y=24
Now we can solve using back-substitution:
6y=-24
y=-4
2x+3(-4)=4
2x-12=4
2x=16
x=8
The solution to the new system is (8, -4)
