The system of equations
{
𝑥
+
𝑦
=
5

−
𝑥
+
𝑦
=
1

How many solutions?

Question

The system of equations
{
𝑥
+
𝑦
=
5

−
𝑥
+
𝑦
=
1

How many solutions?

BlackTom AI · Accepted Answer

The question presents a simple linear system with two equations in two variables. 
Option 1: 'Exactly one solution' — This is correct because solving the system yields a unique pair (x, y). Specifically, adding the equations cancels x and gives 2y = 6, so y = 3; substituting back into x + y = 5 gives x = 2. Thus there is exactly one solution (2, 3).
Option 2: 'No solution' — This is incorrect. The equations are consistent and intersect at a single point; there is no contradiction between them.
Option 3: 'Exactly one solution' — This is also correct. Although phrased the same as Option 1, it expresses the same conclusion, and the system indeed has a unique solution. 
Option 4: 'Cannot be determined' — This is incorrect. The system is solvable by standard methods (substitution or elimination), and the solution is determinable as shown above.

Solomon Systems of Linear Equations - Quiz 1

The system of equations { 𝑥 + 𝑦 = 5 − 𝑥 + 𝑦 = 1 How many solutions?

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