what does it mean for an ordered pair to be a soltuin of both equations?
for example,for this system, is the ordered pair a solution of both equations?
(2,2.4)
4x+5y=20
2x+6y=10
substitute the x and y values of your given point into each of the two equations.
If the statement is true, that is, if it satisfies the equation, then it is a solution for the equations.
oh,ok..
let's say for one equation you get 2=2, and for another, you get 4=4.is the ordered pair a solution of both equations?
yes, both are true statements, so it is a solution.
if one of the equations had given you 3 = 5, then "not"
what if for one equation it's 3=5, and for another it's also 3=5?
then clearly the point is not on either of the two lines.
(each of the given equation has a graph representing a straight line)
ok then thanks
For an ordered pair to be a solution of both equations, it means that when the values of the pair are substituted into both equations, the equations are true.
To determine whether the ordered pair (2,2.4) is a solution of both equations:
1. Substitute the values of x and y from the ordered pair (2,2.4) into the first equation:
4(2) + 5(2.4) = 20
Simplifying this equation, we get:
8 + 12 = 20
20 = 20
Since the equation is true, the ordered pair (2,2.4) is a solution of the first equation.
2. Substitute the values of x and y from the ordered pair (2,2.4) into the second equation:
2(2) + 6(2.4) = 10
Simplifying this equation, we get:
4 + 14.4 = 10
18.4 = 10
Since the equation is not true (18.4 is not equal to 10), the ordered pair (2,2.4) is not a solution of the second equation.
Therefore, the ordered pair (2,2.4) is only a solution of the first equation and is not a solution of the second equation.