Crestview High School Gauss Jordan Elimination Questions

Solve the following 2×2 system of equations by hand using matrices (also known as Gaussian Elimination). That is, transform the augmented matrix into reduced row echelon form (rref – ones on the diagonal and zeros above and below the diagonal). Write your solution as an ordered pair. 4x – 3y = -1 x + 2y = 19

2. Solve the following 3×3 system of equations by hand using matrices (also known as Gauss-
Jordan Elimination). That is, transform the augmented matrix into row echelon form (ref –
ones on the diagonal and zeros below the diagonal), change the reduced matrix back into a
system of equations to solve for all the variables. Write your solution as an ordered triple.
x + y – z= 6
3x – 2y +z = -5
x + 3y – 2z = 14
1. Solve the following 2×2 system of equations by hand using matrices (also known as
Gaussian Elimination). That is, transform the augmented matrix into reduced row echelon
form (rref – ones on the diagonal and zeros above and below the diagonal). Write your
solution as an ordered pair.
4x – 3y = -1
x + 2y = 19
4. Solve the system of equations using the elimination method:
3x – 4y=11
-3x+2y=-7
5. Solve the system of equations using the elimination method:
За – 2b = 2
4a-5b = -2
Solve the following systems of equations using the method of your choice:
6.
x + y = 4
x-y = 5
2
Solve the following application problems:
14. Tickets at a concert were sold to adults for $3.00 and students for $2.00. If the total receipts were $80
and 35 tickets were sold, how many adults and how many student tickets were sold?
5
15. A 90% antifreeze solution is to be mixed with a 75% solution to make 120L of a 78% solution. How
many liters of the 90% and 75% solution will be used?
16. Panera’s recently sold small lemonades for $1.55, medium lemonades for $1.79, and large lemonades
for $2.09. During a lunch-time rush, Corey sold 40 lemonades for a total of $70.70. The number of
small drinks and large drinks, combined, was 10 fewer than the number of medium drinks. How many
drinks of each size were sold?
Chapter 4 and 9
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1. Solve the system of equations graphically:
3
1
y=-x-3
2
11
2x + y = 2
-3
-2
-1
1
2
4
5
x
-1
-2
-3
-4
-5
2. Solve the system of equations using the substitution method:
y=x-5
2x – 5y=1
3. Solve the system of equations using the substitution method:
1
-r + s = 12
2
2r-s=-4
1