A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[-6x+y=-8],[-6x+8y=-22]:} Add to eliminate x. Subtract to eliminate y. Add to eliminate y. Subtract to eliminate x.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[-6x+y=-8],[-6x+8y=-22]:} Add to eliminate  x. Subtract to eliminate  y. Add to eliminate  y. Subtract to eliminate  x.

Bytelearn · Accepted Answer

Analyze Variables for Elimination: Analyze the system of equations to determine which variable can be eliminated with the least amount of work. The system of equations is: -6x + y = -8 -6x + 8y = -22 We can see that the coefficient of x in both equations is the same (-6), but the coefficients of y are different (1 and 8). To eliminate x, we would need to multiply the first equation by a number to make the coefficient of x in the first equation the opposite of the coefficient of x in the second equation. However, since the coefficients of x are already the same (and opposite in sign), we can simply add the two equations together to eliminate x.Perform Addition to Eliminate x: Perform the addition of the two equations to check if x is eliminated. Adding the two equations: (-6x + y) + (-6x + 8y) = -8 + (-22) -6x + y - 6x + 8y = -30 Combine like terms: -12x + 9y = -30 We can see that adding the equations does not eliminate x. This is because we have made a mistake in our calculation. We should have added the y terms, not the x terms, since we are trying to eliminate x.

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