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Graphically solving a System of two Linear Equatio
We will use the fact that the solution
to a system of equations of two variables and
two equations occurs at the point the graph of
the two equations intersect.
Remember that every point (x,y) on
the graph of an equations represents a
ordered x,y pair that is a solution to that
equation. The solution to a system of
equations is the ordered x,y pair that satisfies
both equations. The solution point must lie
on both graphs and the point of intersection is
the only point that does that.
We will now show how to find the
point of intersection. Let us solve the
following system:
4x+3y=14
9x-2y=14
First wemust solvethese equations for y because
we can only enter a y = equation in the calculator
4x+3y=14
3y=14-4x divideboth sides by 3 divideboth sides by -2
We could take more steps to put the
equations above in slope intercept form if we
were graphing them by hand. However that is
not necessary with the calculator.
We will now enter these two equations into the
calculator . Press “y=” to get to the equation screen. Press “clear” to
clear any equations already in the calculator.
The key presses to in enter the two equations into the calculator are
shown above. Notice we use the
key for x shown by the second from the top arrow on the picture to our
left. And we use the parenthesis shown by the third arrow to insure the
14 and -4x are both divided by 3 in the first equation. Finally we use
negative key
shown by the bottom arrow for the negative 2 divisor in the second
equation. We used the
on the right side of the calculator when we wanted to subtract as in
14-4x. But if there is nothing to subtract from and we wish to denote a
negative number or the negative of a variable we must use
.
Study how these two keys are used and make sure you understand when to
use each.
Finally press graph (top arrow) to graph the two equations.
We see the two equations do intersect as shown by the circle. We must
find the intersection.
Our key presses so far are shown below.
We press then
to get to the screen at our left. We
need to find the coordinates of the intersection so we press 5 for
intersection from the menu.
The calculator is asking us which curves we want it to find the
intersection of. If we have cleared all the old equations in the first
step there should only be 2 graphs and so the cursor should be on the
first curve and all we have to do is press enter to confirm that this
one of the curves we want to intersect. Press enter at this time.
Notice the cursor jumped to the next curve and the calculator is
asking us to confirm that this is the other curve we want it to find the
intersection of. Press enter to confirm. So far we have pressed the keys
below.
The calculator is now asking for a guess . You could move the cursor
closer to the intersection using the right arrow (up and down arrows
jump you to other curves, only left and right arrows move you along
curves). The present location of the cursor is close enough for our
purposes. Press enter (the third time in a row) to accept this guess.
The complete list of key presses to solve this system is shown below.
We now have a solution x=2 and y=2. That is the coordinates of the point
of intersection.
divideboth sides by -2
key for x shown by the second from the top arrow on the picture to our
left. And we use the parenthesis shown by the third arrow to insure the
14 and -4x are both divided by 3 in the first equation. Finally we use
negative key
shown by the bottom arrow for the negative 2 divisor in the second
equation. We used the
on the right side of the calculator when we wanted to subtract as in
14-4x. But if there is nothing to subtract from and we wish to denote a
negative number or the negative of a variable we must use
.
Study how these two keys are used and make sure you understand when to
use each.
then
to get to the screen at our left. We
need to find the coordinates of the intersection so we press 5 for
intersection from the menu.
