7x+9y=17 , 6y +9x=23 solve by elimination method

Question

Please solve the problem by using substitution or elmination method

Answer 1

Elimination method

Given equation 7x+9y = 17

multiple to each side by negitive 9.

-63x-81y = -153 ---------> (1)

And 6y+9x = 23

9x+6y = 23

Multiple to each side by 7.

63x+42y = 161 ----------> (2)

To eliminate the x value, add the equtions (1) and (2).

-63x-81y = -153

63x+42y = 161

____________

-39y = 8

Divide to each side by negitive 39.

-39y/39= 8/-39

⇒ y = -8/39

Substitute the y value in (1).

-63x-81*-8/39 = -153

-63x+216/13 = -153

Subtract 216/13 from each side.

-63x+216/13-216/13 = -153 -216/13

-63x = (-1989-216)/13

-63x = -2205/13

Divide to each side by negitive 63.

-63x/-63 = -2205/-63*13

x = -2205/-819

Cancel the signs on right side of equality.

⇒ x = 35/13

Solution x = 35/13, y = -8/39.