# How do you solve the following system?: #61x -31y =-33 , -3x +7y = 8#

##### 1 Answer

#### Explanation:

We have:

#{(61x-31y=-33" "" "" "" "" "mathbf(eq. 1)),(-3x+7y=8" "" "" "" "" "" "color(white)(sl)mathbf(eq. 2)):}#

We want to either cancel out the

#{:(color(white)"-.-"183x-93y=-99" "" "" "" "color(white)(sl)mathbf(eq. 1)xx3),(ul(-183x+427y=488" "+)" "" "color(white)(ss)mathbf(eq. 2)xx61),(color(white)("-------------")334y=389" "" "" "" "" "mathbf(eq. 3)):}#

From

#color(blue)(y=389/334#

We can now plug this value of

#-3x+7color(blue)y=8" "=>" "-3x+7(color(blue)(389/334))=8#

Solving this equation, we multiply

#-3x+2723/334=8#

#-3x=8-2723/334#

Find a common denominator.

#-3x=2672/334-2723/334#

#-3x=-51/334#

#x=-51/334(-1/3)#

The negatives will cancel, so

#color(red)(x=17/334#

Written as the ordered pair

#color(green)(|barul(color(white)(int^int)(x,y)=(17/334,389/334)color(white)(int^int)|))#