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Graphing
Substitution
Elimination
Matrix
Word Problems
100
Graph the equations x + y = 4 AND x - y = 2 and find the intersection point.
(3,1)
100
Solve the system by the substitution method x + y =3 AND x = 2y
(2,1)
100
Solve the system by the elimination method x + y = 7 AND x - y = 3
(5,2)
100
Turn the system into an augmented matrix. Then perform the requested row operation and rewrite the matrix. ONLY DO ONE OPERATION. The system is 4x + 12y -20z = 8 AND x +6y -3z = 7 AND -3x -2y +z = -9. Multiply 3*row2 + row 3 --> row 3
[4 12 -20 8] [1 6 -3 7] [0 16 -8 12]
100
One number is 1? less than a second number. Twice the second number is 12? less than 3? times the first. Find the two numbers.
14 and 15
200
Graph the system x + y = 6 AND -x + y = -6 and find the point of intersection.
(6,0)
200
Solve the system by the substitution method y = 3x +1 AND 4y - 8x = 12
(2,7)
200
Solve the system by the elimination method 6x - y = -5 AND 4x - 2y = 6
(-2, -7)
200
Use back-substitution to solve the system x + y + 2z = 19 AND y +2z =13 AND z = 5
(6,3,5)
200
One number is 3? less than a second number. Twice the second number is 12? more than 3? times the first. Find the two numbers.
-6 and -3
300
Graph the system y = x - 2 AND y = 2x + 3 and find the point of intersection.
(-5,-7)
300
Solve the system by the substitution method 2x - 5y = 1 AND 3x + y = -7
(-2,-1)
300
Solve the system by the elimination method x - 2y = 5 AND 5x - y = -2
(-1,-3)
300
Rewrite the system as a matrix. Then use Gaussian Elimination to put the matrix in row echelon form and use back-substitution to solve. x + 2y = 11 AND x - y = -1
(3,4)
300
Two cars leave a city and head in the same direction. After ? 5 hours, the faster car is 20? miles ahead of the slower car. The slower car has traveled 210? miles. Find the speeds of the two cars.
42 mph and 46 mph
400
Graph the system 2x + y = 4 AND 6x = -3y + 6
no solution
400
Solve the system by the substitution method 1/3x - y =2 AND x -3y = 6
infinite number of solutions (same line)
400
Solve the system by the elimination method. x - 3y = -6 AND 3x - 9y = 9
no solution
400
Rewrite the system as a matrix. Then use Gaussian Elimination to put the matrix in row echelon form and use back-substitution to solve. x + y - z = -2 AND 2x - y + z = 5 AND -x + 2y + 2z = 1
(1,-1,2)
400
A certain aircraft can fly 756? miles with the wind in 3? hours and travel the same distance against the wind in ?7 hours. What is the speed of the wind?
72 mph
500
Graph the system y - 3x = -2 AND 6x -2y = 4
infinite number of solutions. (same line)
500
Solve the system by the substitution method 4x - 24 = 3y AND 9y = 3x - 1
(71/9, 68/27)
500
Solve the system by the elimination method. 2x - 3y = 4 AND 4x +5y = 3
(29/22, -5/11)
500
Rewrite the system as a matrix. Then use Gaussian Elimination to put the matrix in row echelon form and use back-substitution to solve. 3y - z = -1 AND x + 5y - z = -4 AND -3x + 6y + 2z =11
(-3,0,1)
500
A chemist needs 90? milliliters of a 20?% solution but has only 4?% and 40?% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
50ml of 4%, 40ml of 40%