Question

5x - 5y = 10
3x - 2y = 2

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)
can someone help me with these steps please?

Answer 1

5x - 5y = 10 ---- (1)
3x - 2y = 2 ---- (2)

Part A:
Let us replace the second equation by the sum of the second equation and 1/5 x the first equation:
(1) * 1/5 = x - y = 2
(2): 3x - 2y = 2
Add:
4x - 3y = 4 ---- (3)

Part B:
Solve equations (1) and (2) for x and y.
Solve equations (1) and (3) for x and y.

Prove they are the same.

Answer 2

ok?

Answer 3

What did you get for x and y after solving equations (1) and (2)?

Answer 4

I don't know how to solve, can u teach me

Answer 5

thank you so that is part a, so now I need to use -2/3 and -8/3 to solve b?

Answer 6

I will solve the equations (1) and (2). You use the same method to solve (1) and (3).
5x - 5y = 10 ---- (1)
3x - 2y = 2 ---- (2)
Let us eliminate x. To do that multiply (1) by 3 and (2) by 5 and subtract:
(1) * 3 = 15x - 15y = 30
(2) * 5 = 15x - 10y = 10
subtract:
0 - 5y = 20
divide by -5:
y = 20/(-5) = -4
Put y in (1) and solve for x:
5x - 5(-4) = 10
5x + 20 = 10
5x= 10 - 20 = -10
x = -2

Solutions are x = -2; y = -4

Answer 7

Part A has already been answered in my very first reply.
The equivalent system of equations we created were:
5x - 5y = 10 and
4x - 3y = 4

For Part B) you need to solve the two original equations given in the problem, namely,
5x - 5y = 10 and 3x - 2y = 2
I have done that above and got x = -2 and y = -4.

There is another thing you have to do for part B):
Solve
5x - 5y = 10 and
4x - 3y = 4

and prove you get the same solution: x = -2 and y = -4.

Answer 8

ok thanks

Answer 9

Can someone help me with part b. I solved some of it but now im stuck. I got 20x-20y=40 and 20x-15y=20. what do I do next?