Question

Can someone check a few problems??? I am not sure if I did them the right way...

Answer 1

QUESTION:

A system of equations is shown below:

8x + 5y = 9
3x + 2y = 4

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:

Part A:
8x + 5y = 9
3x + 2y = 4

I chose to eliminate y so,
5y(2) = 10y
2y(5) = 10y
Now the equations look like this:
8x + 10y = 9
3x + 10y = 4
I have to subtract the equations now and I get:
8x - 3x = 5x
10y - 10y = 0 (y is eliminated)
9 - 4 = 5
So, 5x = 5
Now I have to divide both sides by 5 and my answer will be:
x = 1

Part B:
8x + 5y = 9
3x + 2y = 4
To get rid of x,
The only common factor of 8 and 3 is 24 so,
8x(3) = 24x
3x(8) = 24x
The new equation would look like this:
24x + 5y = 9
24x + 2y = 4
Subtract the equations:
24x - 24x = 0 (x is eliminated)
5y - 2y = 3y
9 - 4 = 5
So, 3y = 5
Divide both sides by 3y:
y = 1.7