Question

A system of equations is given.

Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7

Explain how to eliminate x in the system of equations.

Answer 1

First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, we have to multiply Equation 1 by 9 and Equation 2 by -4.

9(4x - 6y = 10) is equivilant to 36x - 54y = 90

-4(9x + 2y = 7) is equivilant to -36x - 8y = -28

Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:

-62y = 62 we have successfully eliminated x!

The last step will be to divide both sides by -62

-62y/-62 = 62/-62

y = -1

Answer 2

Explanation:

multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.

in our case the least common multiple of 4 and 9 is 36.

so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract

36x - 54y = 90

- 36x + 8y = 28

-------------------------

0 -62y = 62

so, x is "eliminated", and we can solve for y : y = -1.

and then we can use one of the original equations to solve for x.

e.g.

9x + 2×-1 = 7

9x - 2 = 7

9x = 9

x = 1