A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[-2x+10 y=72],[-6x+10 y=36]:} Add to eliminate y. Subtract to eliminate x. Add to eliminate x. Subtract to eliminate y.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[-2x+10 y=72],[-6x+10 y=36]:} Add to eliminate  y. Subtract to eliminate  x. Add to eliminate  x. Subtract to eliminate y.

Bytelearn · Accepted Answer

Analyze Coefficients: Analyze the coefficients of the variables in both equations. We have the system of equations: -2x + 10y = 72 -6x + 10y = 36 To eliminate a variable, we need to make the coefficients of either x or y the same with opposite signs so that addition or subtraction will cancel out that variable.Compare Coefficients: Compare the coefficients of x and y in both equations. The coefficients of y are already the same (10 and 10), but the coefficients of x are not the same (-2 and -6). To eliminate y, we would need to multiply the first equation by a factor that would make the coefficient of y in the first equation the opposite of the coefficient of y in the second equation. However, since the coefficients of y are already the same, we can simply subtract one equation from the other to eliminate y.Decide Operation: Decide on the operation to eliminate y. Since the coefficients of y are the same, we can subtract the second equation from the first to eliminate y. -2x + 10y = 72 - (-6x + 10y = 36) This will result in: -2x + 10y - (-6x + 10y) = 72 - 36Perform Subtraction: Perform the subtraction to check if y is eliminated. -2x + 10y - (-6x + 10y) = 72 - 36 simplifies to: -2x + 10y + 6x - 10y = 72 - 36 The terms +10y and -10y cancel each other out, leaving: 4x = 36

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