Question

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied? First equation: 4x − 3y = 34 Second equation: 3x + 2y = 17
A.The first equation should be multiplied by 2 and the second equation by 3.
B.The first equation should be multiplied by 2 and the second equation by −3.
C.The first equation should be multiplied by 3 and the second equation by 4.
D.The first equation should be multiplied by 3 and the second equation by −4.

Answer 1

4x - 3y = 34
3x + 2y = 17

first equation should be multiplied by 2...second equation should be multiplied by 3

Answer 2

To eliminate the y terms and solve for x in the fewest steps, "The first equation should be multiplied by 2 and the second equation by 3".

To eliminate Terms

To eliminate Terms we need to make the coefficient of any terms equal we need to take the LCM of the coefficient and then try to make the coefficient equal to the LCM by multiplying the complete equations.

Given to us

First equation: 4x − 3y = 34

Second equation: 3x + 2y = 17

Solution

To eliminate y from both the equations the like terms of y should be eliminated, therefore, the coefficient of the y terms should be made equal.

$4x -3y = 34\\3x + 2y = 17$

In the equations, the coefficient of the y terms is 3 and 2, and the LCM of this two is 6.

2 | 3, 2

3 |  3,1

  |  1, 1

LCM = 3 x 2 = 6

To make the coefficient of y in both the terms as 6, we need to multiply the equation with 2 and the second equation with 3,

Verification

$2(4x -3y = 34)\\3(3x + 2y) = 17$

$8x -6y = 68\\9x + 6y = 51$

After adding the first equation to the second we get.

$8x -6y = 68\\9x + 6y = 51\\\\(8x+9x)+(-6x+6x) = (68+51)\\17x = 119$

Hence, To eliminate the y terms and solve for x in the fewest steps, "The first equation should be multiplied by 2 and the second equation by 3".

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