3x + 8y = 12 2x + 2y = 3 Part A: Create an equivalent system of equations by replacing one equation with the sum of that equatio
n 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)
Ok here is what I think. Let us first number these statements, as #1, and #2. First statement: 3x + 8y = 12 (1) Second Statement: 2x + 2y = 3 (2) Now, we can work from this. We want to make one of the equations be equal to 0 so that at the end when we check they can be equal to each other. Let us use 4. 3x+8y=12 1-8x-8y=-12 2 This gives us:-5x = 0 Now we should try and isolate x so we can substitute it into one of the equations. We have -5x=0 and x=0 3(0)+8y=12 8y=12 y=12/8 y=3/2 Plug in these new equations y=3/2 and y=0 into any of the first equations 3x+8y=12 3(0)+8(3/2)= 12 8(3/2)=12 4(3)=12 12=12 Now we know it works, thats our check^^
