Algebra III Academic
Calculator Applications – Solving Systems of Equations
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Solve systems of equations
Solve system application problems
Method I: Graphing
1. Carefully solve each equation for y.
2. Turn on your calculator and press the “y =” button.
3. Put the right side of one of the equations into y1.
4. Put the right side of the other equation into y2.
5. Press “zoom 6” to get a standard viewing window.
6. Manipulate the window to show where the two lines intersect.
7. Calculate the intersection point (this is the solution point).
Solve the systems by graphing.
1) −4x − 2y = −12
4x + 8y = −24
2) 4x + 8y = 20
−4x + 2y = −30
3) x + y = 2
3x + 4y + z = 17
x + 2y + 3z = 11
Method II: Matrices – When graphing is not an option or if you would rather NOT graph.
1. Now we will solve the system of equations
in 3) that we could not solve by using the
graphing method.
2. Turn on calculator and access the matrix
press 2nd x^-1 .
3. The screen should look like this. Scroll to
the right and choose edit.
4. Press 1 to edit matrix A.
5. You are now prompted to enter the
dimensions of the matrix A; enter the
number of rows and the number of columns.
6. To enter each number, select the correct
location using the arrow buttons, enter the
number and scroll left/right until all numbers
are entered.
7. Press 2nd MODE and then press 2nd x^-1 to
return to the matrix screen.
8. Arrow to the right and choose MATH.
Scroll down the menu and choose rref( by
pressing enter. Then press 2nd x^-1
and choose matrix A. Press enter and this
screen will display. This is a reduced row
matrix screen and gives the values for x, y,
and z.
9. ( - 10, 12, - 1) is the solution to the system.
Algebra III Academic
Calculator Applications – Solving Systems of Equations
Classwork/Homework:
Solve the systems of equations that follow.
A.
3 + 2x = y
− 3 – 7y = 10x
B.
- 14 = - 20 y – 7x
10y + 4 = 2x
C.
–x − y – 3z = – 9
−3x – 1 = z
x = 5y − z + 23
D.
4x + 4y + z = 24
2x − 4y + z = 0
5x − 4y − 5z = 12
E.
−7x − 8y = 9
−4x + 9y = −22
F.
−4x − 2y = 14
−10x + 7y = −25
G.
−x − 5y + z = 17
−5x − 5y + 5z = 5
2x + 5y − 3z = −10
H.
4r − 4s + 4t = −4
4r + s − 2t = 5
−3r − 3s − 4t = −16
I.
5x + 4y = −30
3x − 9y = −18
J.
3x − 2y = 2
5x − 5y = 10
K.
x = – 4z – 19
y = 5x + z – 4
− 5y − z = 25
L.
x − 6y + 4z = −12
x + y − 4z = 12
2x + 2y + 5z = −15
3y - 4 = 2 ( x +1)
-3x - 5y =15
x=4
Domain: __________
Domain: __________
Domain: ___________
Range:
Range:
Range:
__________
___________
____________
x – intercepts: ________
x – intercepts: ________
x – intercepts: ________
y – intercept: _________
y – intercept: _________
y – intercept: _________
y - 2 = 3x 2 - 6x
y = 5x
y = -2x 2 - 6x + 2
Domain: _____________
Domain: __________
Domain: ___________
Range:
Range:
Range:
_____________
___________
____________
x – intercepts: ________
x – intercepts: ________
x – intercepts: ________
y – intercept: _________
y – intercept: _________
y – intercept: _________
Vertex: ______________
Vertex: ______________
Vertex: ______________
Axis of Symmetry: _____
Asymptote: __________
Axis of Symmetry: _____
Write the slope-intercept form of the equation of the line through (5, 13) and (−4, −1).
a. Evaluate the equation when x = 3
b. What is the x – intercept?
Write the equation of an exponential function that passes through (1, 4) and (3, 12 ).
c. Evaluate the equation when x = 10.
d. What is the y-intercept?
Write the equation of a quadratic function that passes through (1, 0), (2.5, 8) and (4, 0).
e. Evaluate when x = 0.
f. What is the vertex?
g. What is the line of symmetry?