A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[3x+6y=45],[3x-7y=-46]:} Add to eliminate x. Subtract to eliminate x. Subtract to eliminate y. Add to eliminate y.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[3x+6y=45],[3x-7y=-46]:} Add to eliminate  x. Subtract to eliminate  x. Subtract to eliminate  y. Add to eliminate  y.

Bytelearn · Accepted Answer

Analyze Variables: Analyze the system of equations to determine which variable can be eliminated with the least amount of work. We have the system: {:[3x+6y=45],[3x-7y=-46]:} To eliminate a variable, we look for coefficients that are the same or opposites. Here, the coefficients of x in both equations are the same (3 and 3).Elimination Operation: Decide on the operation to use for elimination. Since the coefficients of x are the same, we can subtract one equation from the other to eliminate x.Check Elimination: Perform a quick check to ensure that subtraction will indeed eliminate the variable x. (3x + 6y) - (3x - 7y) = 45 - (-46) 3x - 3x + 6y + 7y = 45 + 46 0x + 13y = 91 This confirms that subtracting the two equations will eliminate x.

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