Question

A system of equations is shown below:

3x + 8y = 12
2x + 2y = 3

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

Answer 1

for Part A would i do elimination?
6x+16y=24
-6x-6y=-9
10y=15
y=1.5?

Answer 2

You need to solve the equation only in Part B.

Answer 3

For Part A: "replacing one equation with the sum of that equation and a multiple of the other"

replace first equation by sum of the first equation and some constant times the second equation. After that,
replace second equation by sum of the second equation and some constant times the first equation.

Answer 4

You can choose the constant as 2.

Replace (3x + 8y = 12) by (3x + 8y = 12) + 2 * (2x + 2y = 3)
Simplify the above.

Answer 5

(3x+8y=12)+(4x+4y=6)
7x+12y=18?

Answer 6

Correct.

Answer 7

so that will be the equation for part A?

Answer 8

You have to do a similar operation with the second equation.
replace second equation by sum of the second equation and some constant times the first equation.

Answer 9

Replace (2x + 2y = 3) by (2x + 2y = 3) + 2 * (3x + 8y = 12)

Answer 10

(2x+2y=3)+(6x+16y=24)
8x+18y=27

Answer 11

Part A) The equivalent system of equations are:
7x +12y =18
8x +18y = 27

Answer 12

so the equivalent systems of equations will be
8x+18y=27
7x+12y=18
Now find the value for x and y?

Answer 13

Part B) First solve the original system of equations.
Then solve the equivalent system of equations created in part A.
Prove the solutions for x and y are the same in both cases.

Answer 14

Original system of equations:
3x + 8y = 12
2x + 2y = 3

Multiply second equation by -4 and add it to the first. Solve for y.

Answer 15

solve for x. (i meant)

Answer 16

i got x=0?

Answer 17

Yes. Sub x = 0 in the second equation and find y.

Answer 18

oh lol thought i made a mistake y=1.5

Answer 19

(0,1.5) for original system

Answer 20

Correct. Or in fractions: (0, 3/2).

Solve the equivalent system created in part A.

Answer 21

8x+12y=18
8x+18y=27

Answer 22

no
7x+12y=18
8x+18y=27

Answer 23

-54x-96y=-144
54x+144y=216
48y=72
y=1.5

Answer 24

7x+12(1.5)=18
7x+18=18
7x=0
x=0

Answer 25

you got the correct y, but 7 * 8 = 56 (not 54)

Answer 26

oops my mistake

Answer 27

-56x-96y=-144
56x+144y=216
48y=72
y=1.5

Answer 28

yes thats what i meant hit 4 on accident and copied for the second equation

Answer 29

thank you

Answer 30

you are welcome.