Question

On a coordinate plane, a line goes through points (2, 4) and (3, 1).
Which are solutions of the linear equation?
Select all that apply.

3x + y = 10

(1, 6)
(2, 4)
(3, 1)
(4, –1)
(5, –5)

Answer 1

To determine which points are solutions of the linear equation \( 3x + y = 10 \), we can substitute the x-coordinates of each point into the equation and check if the corresponding y-coordinate satisfies the equation.

1. **For the point (1, 6)**:
\[
3(1) + 6 = 3 + 6 = 9 \quad (\text{not } 10)
\]
Not a solution.

2. **For the point (2, 4)**:
\[
3(2) + 4 = 6 + 4 = 10 \quad (\text{equals } 10)
\]
This is a solution.

3. **For the point (3, 1)**:
\[
3(3) + 1 = 9 + 1 = 10 \quad (\text{equals } 10)
\]
This is a solution.

4. **For the point (4, -1)**:
\[
3(4) + (-1) = 12 - 1 = 11 \quad (\text{not } 10)
\]
Not a solution.

5. **For the point (5, -5)**:
\[
3(5) + (-5) = 15 - 5 = 10 \quad (\text{equals } 10)
\]
This is a solution.

Thus, the points that are solutions of the equation \( 3x + y = 10 \) are:
- (2, 4)
- (3, 1)
- (5, -5)

Final answer: **(2, 4)**, **(3, 1)**, **(5, -5)**.