Answer:
1) Yes
2) No
Step-by-step explanation:
Substitute the x and y values of the given points into the equation and solve. If the result is a true statement, then they are solutions.
1) First, substitute the x and y values of (1,1.5) for the x and y in the given equation. Then, solve. (You can convert 1.5 from a decimal to a fraction, making it [tex]\frac{3}{2}[/tex].)
[tex]1.5= \frac{1}{4} (1) + \frac{5}{4} \\\frac{3}{2} = \frac{1}{4} +\frac{5}{4} \\\frac{3}{2} = \frac{6}{4} \\\frac{3}{2} = \frac{3}{2}[/tex]
The result is a true statement. Thus, (1, 1.5) is a solution to the equation.
2) Do the same with the point (12,4):
[tex]4 = \frac{1}{4} (12) + \frac{5}{4} \\4 = 3 + \frac{5}{4} \\4 = \frac{12}{4} +\frac{5}{4} \\4 \neq \frac{17}{4}[/tex]
The result is a false statement. The two values are not equal. Thus, (12,4) is not a solution to the equation.
