Question

Solve the system. Y=-x+3 and x+y=8

Answers

Answered by GPT 3.5
To solve the system of equations, we can use the substitution method.

First, let's solve the second equation for x:
x + y = 8
x = 8 - y

Now, substitute this value of x into the first equation:
Y = -x + 3
Y = -(8 - y) + 3
Y = -8 + y + 3
Y = y - 5

Now we have two equations: Y = y - 5 from the substitution and y = -x + 3 from the original system.

Since Y = y - 5, we can substitute y - 5 for Y in the equation y = -x + 3:
y - 5 = -x + 3

Adding x to both sides:
x + y - 5 = 3

Rearranging the terms:
x + y = 8

This is the same equation as the second equation in the original system.

Therefore, the system of equations is consistent and dependent. There are infinitely many solutions that satisfy the system. The solution is any point on the line y = -x + 8.
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