A system of equations is shown below:

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.

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

Question

A system of equations is shown below:

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. 

Part B: Show that the equivalent system has the same solution as the original system of equations.

anonymous · Answer

@nikato

triciaal · Answer

the first eqn is the same as x - y = 2  if you divide everything by 5

anonymous · Answer

5x-5y+5y=10+5y
5x=5y+10
___________
      5
x=y+2

triciaal · Answer

x - y = 2   eqn 1
3x -2y = 2    eqn 2
multiply eqn 1 by -2
-2x +2y = -4   eqn 3
add eqn 2 and eqn 3
x = -2
put this value of x in either eqn to find y
using eqn 1 
-2 -y = 2  rearrange to get y = -4

x = -2 and y = -4
substitute in original eqn
left hand side
5x -5y = 5(-2) - 5(-4) = -10 + 20 = 10
right hand side = 10
10 = 10

triciaal · Answer

@RosieF any questions?