to eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be…

to eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?\nfirst equation: 4x - 3y = 34\nsecond equation: 3x + 2y = 17\nthe first equation should be multiplied by 2 and the second equation by 3.\nthe first equation should be multiplied by 2 and the second equation by -3.\nthe first equation should be multiplied by 3 and the second equation by 4.\nthe first equation should be multiplied by 3 and the second equation by -4.

to eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?\nfirst equation: 4x - 3y = 34\nsecond equation: 3x + 2y = 17\nthe first equation should be multiplied by 2 and the second equation by 3.\nthe first equation should be multiplied by 2 and the second equation by -3.\nthe first equation should be multiplied by 3 and the second equation by 4.\nthe first equation should be multiplied by 3 and the second equation by -4.

Answer

Explanation:

Step1: Analyze the coefficients of (y)

The coefficient of (y) in the first equation is (-3), and in the second equation is (2).

Step2: Find the least - common multiple

The least - common multiple of (3) and (2) is (6).

Step3: Check the options

  • If we multiply the first equation (4x - 3y=34) by (2), we get (8x-6y = 68).
  • If we multiply the second equation (3x + 2y=17) by (3), we get (9x+6y = 51).
  • Then adding these two new equations ((8x-6y)+(9x + 6y)=68 + 51), the (y) terms are eliminated.

Answer:

The first equation should be multiplied by (2) and the second equation by (3).