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System 
A
System 
B



{[6x-5y=1],[-2x+2y=-1]:}

{[4x-3y=0],[-2x+2y=-1]:}





How can we get System 
B from System 
A ?

Choose 1 answer:
A) Replace one equation with the sum/difference of both equations
(B) Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations
(C) Replace one equation with a multiple of itself
Deplace one equation with a multiple of the other equation

 \space \space \spaceSystem A  \space \space \space \space \space \space \space \space \space \space \space \space \space \space \spaceSystem B\newline\newline{[6x5y=1]}\{[6x-5y=1]\}, \space \space \space \space \space{[4x3y=0]}\{[4x-3y=0]\}\newline{[2x+2y=1]}\{[-2x+2y=-1]\},{[2x+2y=1]}\{[-2x+2y=-1]\}\newline\newlineHow can we get System B from System A ?\newlineChoose 11 answer:\newlineA) Replace one equation with the sum/difference of both equations\newlineB) Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations\newlineC) Replace one equation with a multiple of itself\newlineD) Replace one equation with a multiple of the other equation

Full solution

Q.  \space \space \spaceSystem A  \space \space \space \space \space \space \space \space \space \space \space \space \space \space \spaceSystem B\newline\newline{[6x5y=1]}\{[6x-5y=1]\}, \space \space \space \space \space{[4x3y=0]}\{[4x-3y=0]\}\newline{[2x+2y=1]}\{[-2x+2y=-1]\},{[2x+2y=1]}\{[-2x+2y=-1]\}\newline\newlineHow can we get System B from System A ?\newlineChoose 11 answer:\newlineA) Replace one equation with the sum/difference of both equations\newlineB) Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations\newlineC) Replace one equation with a multiple of itself\newlineD) Replace one equation with a multiple of the other equation
  1. Analyze System A and System B: Analyze System A and System B to identify differences and similarities.\newlineSystem A: \newline11. 6x5y=16x - 5y = 1\newline22. 2x+2y=1-2x + 2y = -1\newlineSystem B:\newline11. 4x3y=04x - 3y = 0\newline22. 2x+2y=1-2x + 2y = -1
  2. Focus on Transformation: Notice that the second equation in both systems is identical. Focus on transforming the first equation of System A to match the first equation of System B.
  3. Compare Coefficients: Compare the coefficients of xx and yy in the first equations of both systems:\newlineSystem A: 6x5y=16x - 5y = 1\newlineSystem B: 4x3y=04x - 3y = 0\newlineWe need to find a transformation that changes 6x5y=16x - 5y = 1 to 4x3y=04x - 3y = 0.
  4. Find Scalar Multiple: Attempt to find a scalar multiple that can be applied to the first equation of System A to achieve the first equation of System B.\newlineLet's try multiplying the first equation of System A by a factor kk:\newlinek(6x5y)=k(1)k(6x - 5y) = k(1)\newlineWe need k(6x5y)k(6x - 5y) to equal 4x3y4x - 3y.
  5. Solve for kk: Solve for kk:k×6x=4xk \times 6x = 4x and k×5y=3yk \times -5y = -3yk=46=23k = \frac{4}{6} = \frac{2}{3} and k=35=35k = \frac{-3}{-5} = \frac{3}{5}These values of kk are not consistent, indicating a mistake in the approach or calculation.