Solve by elimination ... SHOW YOUR WORK. - 3x + 2y = 18

-9x - 5y=21

x = - 4, y = 3

Step-by-step explanation:

-3x + 2y = 18 (1)

-9x - 5y = 21 (2)

To solve by eliminating, the coefficients of either x or y must be the same in both equation.

Now let us make the coefficient of x in both equation to be the same. To do this, multiply equation (1) by the coefficient of x in equation (2) ie - 9, and multiply equation (2) by the coefficient of x in equation (1) ie - 3 this is illustrated below:

-9 (-3x + 2y = 18)

27x - 18y = - 162 (3)

-3 (-9x - 5y = 21)

27x + 15y = - 63 (4)

Now, subtract equation 4 from equation 3

27x - 18y = - 162

- (27x + 15y = - 63)

-33y = - 99

Divide both side by - 33

y = - 99/-33

y = 3

Now we substitute the value of y into any of the equation to obtain x. In this case, let use equation 4

27x + 15y = - 63

27x + 15 (3) = - 63

27x + 45 = - 63

Collect like terms

27x = - 63 - 45

27x = - 108

Divide both side by 27

x = - 108/27

x = - 4

Therefore, x = - 4, y = 3