Question

Solve these using elimination.1)x = 5 - 9y4x + 9y = -72)3x = 5y - 92y = 3x + 33)10x - 5 = 3y2x - 3y = 14)-6x - 4y = 10-12x - y = 13

Answer 1

X + 9y = 5 .....multiply by -1
4x + 9y = -7
-----------------
-x - 9y = -5 (result of multiplying by -1)
4x + 9y = -7
----------------add
3x = -12
x = -12/3
x = -4

x = 5 - 9y
-4 = 5 - 9y
-4 - 5 = - 9y
-9 = - 9y
-9/-9 = y
1 = y

solution is (-4,1)
====================
3x = 5y - 9
-3x = -2y + 3 ....I rearranged this equation from 2y = 3x + 3
----------------add
0 = 3y - 6
6 = 3y
6/3 = y
2 = y

3x = 5y - 9
3x = 5(2) - 9
3x = 10 - 9
3x = 1
x = 1/3

solution is (1/3,2)
====================
10x - 3y = 5....rearranged from 10x - 5 = 3y
2x - 3y = 1...multiply by -1
---------------
10x - 3y = 5
-2x + 3y = -1 (result of multiplying by -1)
---------------add
8x = 4
x = 4/8
x = 1/2

10x - 5 = 3y
10(1/2) - 5 = 3y
5 - 5 = 3y
0 = 3y
0 = y

solution is (1/2,0)
======================
-6x - 4y = 10....multiply by -2
-12x - y = 13
----------------
12x + 8y = -20 (result of multiplying by -2)
-12x - y = 13
-----------------add
7y = - 7
y = -7/7
y = -1

-6x - 4y = 10
-6x - 4(-1) = 10
-6x + 4 = 10
-6x = 10 - 4
-6x = 6
x = -6/6
x = -1

solution is (-1,-1)