# How do you solve the following system?: 6x - 4y = 3 , 6x+5y=18

Mar 15, 2018

x = $\frac{29}{18}$

y = $\frac{5}{3}$

#### Explanation:

6x - 4y = 3 -------------(1)

6x + 5y = 18 -----------(2)

taking equation (2) - (1), we get

5y - (-4y) = 18 - 3

9y = 15

dividing through by 9 gives,

y = $\frac{5}{3}$

Substituting the value of y into equation (1) gives,

6x - 4$\left(\frac{5}{3}\right)$ = 3

6x = $\frac{20}{3}$ + 3

6x = $\frac{29}{3}$

Dividing through by 6 gives,

x = $\frac{29}{3}$$\cdot$$\frac{1}{6}$

x = $\frac{29}{18}$