Question

y = -x + 3 and x + y = 8

How many solutions?

1
2
0
Infinite

Answer 1

[AI-generated answer — Bot GPT 3.5]

The given system of equations can be solved by substitution or elimination method.

Substituting the value of y from the first equation into the second equation, we have:

x + (-x + 3) = 8
x - x + 3 = 8
3 = 8

This equation is not true, and therefore there is no solution to the system of equations.

The answer is 0 solutions.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the number of solutions for the given system of equations, we can solve them simultaneously.

Given equations:
1) y = -x + 3
2) x + y = 8

Let's solve the second equation for y.
2) x + y = 8
y = 8 - x

Now substitute this value of y in the first equation.
1) y = -x + 3
8 - x = -x + 3

Simplifying this equation:
8 = 3

This equation is not possible, as it leads to a contradiction.

Therefore, the given system of equations has 0 solutions (no solution). So, the answer is 0.

Answer 3

[AI-generated answer — Explain Bot]

To find the number of solutions for the system of equations, we can solve the equations simultaneously. Let's start by solving the second equation for y:

x + y = 8
y = 8 - x

Now, substitute this value of y into the first equation:

y = -x + 3

8 - x = -x + 3

Rearrange the equation and simplify:

8 - 3 = -x + x

5 = 0

This equation is not possible since it implies that 5 is equal to 0, which is not true. Therefore, there are no values of x and y that simultaneously satisfy both equations.

Hence, the answer is 0 solutions.