Find the ordered pair that is a solution to the graphs
a) (3,7)
We substitute the first number of the ordered pair, which is 3,
in place of x and the second number, which is 7, in place of y
in both equations and simplify.
Substituting 3 for x, and 7 for y in the first one:
That's a false equation because 7 does not equal 9.
So the ordered paie (3.7) is not a solution to .
Substituting 3 for x, and 7 for y in the second one:
That's a false equation because 7 does not equal 1.
So the ordered paie (3.7) is not a solution to the
equation .
So the ordered pair (3,7) is not a solution to
because it is not a solution
to either one of the equations, so it cannot be a solution
to both.
If what we had ended up with in BOTH cases had been true equations,
then the ordered pair would have been a solution. But in this
case they were both false, so the ordered pair (3,7) is not a
solution to .
b) (0,7)
We substitute the first number of the ordered pair, which is 0,
in place of x and the second number, which is 7, in place of y
in both equations and simplify.
Substituting 0 for x, and 7 for y in the first one:
That's a false equation because 7 does not equal 3.
So the ordered paie (0.7) is not a solution to .
Substituting 0 for x, and 7 for y in the second one:
That's a false equation because 7 does not equal 1.
So the ordered paie (3.7) is not a solution to the
equation .
So the ordered pair (3,7) is not a solution to
because it is not a solution
to either one of the equations, so it cannot be a solution
to both.
If what we had ended up with in BOTH cases had been true equations,
then the ordered pair would have been a solution. But in this
case they were both false, so the ordered pair (0,7) is not a
solution to .
c) (7,2)
We substitute the first number of the ordered pair, which is 7,
in place of x and the second number, which is 2, in place of y
in both equations and simplify.
Substituting 7 for x, and 2 for y in the first one:
That's a false equation because 2 does not equal 17.
So the ordered paie (7.2) is not a solution to .
Substituting 7 for x, and 2 for y in the second one:
That's a false equation because 2 does not equal 5.
So the ordered paie (7.2) is not a solution to the
equation .
So the ordered pair (7,2) is not a solution to
because it is not a solution
to either one of the equations, so it cannot be a solution
to both.
If what we had ended up with in BOTH cases had been true equations,
then the ordered pair would have been a solution. But in this
case they were both false, so the ordered pair (7,2) is not a
solution to .
d) (-5, -7)
We substitute the first number of the ordered pair, which is -5,
in place of x and the second number, which is -7, in place of y
in both equations and simplify.
Substituting -5 for x, and -7 for y in the first one:
That's a true equation because -7 does equal -7.
So the ordered paie (-5.-7) is a solution to .
Substituting -5 for x, and -7 for y in the second one:
That's a true equation because -7 does equal -7.
So the ordered paie (3.7) is a solution to the
equation .
So the ordered pair (3,7) is a solution to
because it is a solution
to BOTH of the equations.
So the correct choice is (d).
The significance of this is that if we graph both lines,
by plotting points, we get this.
We see that the point that is on both lines is the point
whose set of coordinates is the ordered pair (-5,-7), the
point where the two lines cross. That's because if you draw
a green vertical line and a green horizontal line through
the point where the two red lines cross, like this:
that the vertical line crosses the x-axis at -5 and the
horizontal line crosses the y-axis at -7.
Edwin