Pierce Frazier
07/26/2024 · Primary School
verify \( (0,2) \) and \( (-1,3) \) are solutions of \( x+2 y=4 \)
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Tutor-Verified Answer
Step-by-step Solution
To verify whether the points \( (0,2) \) and \( (-1,3) \) are solutions of the equation \( x + 2y = 4 \), we will substitute the coordinates of each point into the equation and check if the equation holds true.
1. **For the point \( (0,2) \)**:
- Substitute \( x = 0 \) and \( y = 2 \) into the equation:
\[
0 + 2(2) = 4
\]
- Simplifying the left side:
\[
0 + 4 = 4
\]
- Since both sides are equal, \( (0,2) \) is a solution of the equation.
2. **For the point \( (-1,3) \)**:
- Substitute \( x = -1 \) and \( y = 3 \) into the equation:
\[
-1 + 2(3) = 4
\]
- Simplifying the left side:
\[
-1 + 6 = 5
\]
- Since \( 5 \neq 4 \), \( (-1,3) \) is not a solution of the equation.
In conclusion, \( (0,2) \) is a solution of the equation \( x + 2y = 4 \), while \( (-1,3) \) is not.
Quick Answer
\( (0,2) \) is a solution, \( (-1,3) \) is not.
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