Solve each system by using the elimination method. Make sure to write your answer in (x,y) form.
1.) 3x-5y=2
2x+5y=13
2.) 3x+11y=4
-2x-5y=9
1.)
3 x - 5 y = 2 Add 5y to both sides
3 x - 5 y + 5 y = 2 + 5 y
3 x = 2 + 5 y Subtract 2 to both sides
3 x - 2 = 2 + 5 y - 2
3 x - 2 = 5 y
5 y = 3 x - 2
2 x + 5 y = 13
2 x + 3 x - 2 = 13
5 x - 2 = 13 Add 2 to both sides
5 x - 2 + 2 = 13 + 2
5 x = 15 Divide both sides by 5
5 x / 5 = 15 / 5
x = 3
3 x - 5 y = 2
3 * 3 - 5 y = 2
9 - 5 y = 2 Add 5 y to both sides
9 + 2 - 5 y + 5 y = 2 + 5 y
9 = 2 + 5 y Subtract 2 to both sides
9 - 2 = 2 + 5 y - 2
7 = 5 y
5 y = 7 Divide both sides by 5
5 y / 5 = 7 / 5
y = 7 / 5
x = 3 , y = 7 / 5
In ( x , y ) form :
( 3 , 7 / 5 )
2.)
3 x + 11 y = 4 Subtract 3 x to both sides
3 x + 11 y - 3 x = 4 - 3 x
11 y = 4 - 3 x Divide both sides by 11
11 y / 11 = ( 4 - 3 x ) / 11
y = ( 4 - 3 x ) / 11
- 2 x - 5 y = 9 Multiply both sides by -1
- 2 x * ( - 1 ) - 5 y * ( - 1 ) = 9 * ( - 1 )
2 x + 5 y = - 9
2 x + 5 * ( 4 - 3 x ) / 11 = - 9
2 x * 11 / 11 + 5 * ( 4 - 3 x ) / 11 = - 9
22 x / 11 + ( 20 - 15 x ) / 11 = - 9
22 x / 11 + 20 / 11 - 15 x / 11 = - 9
7 x / 11 + 20 / 11 = - 9 Multiply both sides by 11
7 x * 11 / 11 + 20 * 11 / 11 = - 9 * 11
7 x + 20 = - 99 Subtract 20 to both sides
7 x + 20 - 20 = - 99 - 20
7 x + 20 - 20 = - 99 - 20
7 x = - 119 Divide both sides by 7
7 x / 7 = - 119 / 7
x = - 17
3 x + 11 y = 4
3 * ( - 17 ) + 11 y = 4
- 51 + 11 y = 4 Add 51 to both sides
- 51 + 11 y + 51 = 4 + 51
11 y = 55 Divide both sides by 11
11 y / 11 = 55 / 11
y = 5
x = - 17 , y = 5
In ( x , y ) form :
( - 17 , 5 )