System of Equations Using Elimination

Question

3x-4y=19

2x-2y=13

Answer 1

3x - 4y = 19

2x - 2y = 13

Multiply the second equation by -2:

3x - 4y = 19

-4x +4y = -26

Add the equations: -x = -7

So, x = 7 and 3(7) - 4y = 19

-4y = -2

So, y = 1/2

Answer 2

3x - 4y = 19

2x - 2y = 13

Multiply the first equation by -1/2 to get:

-3x/2 + 2y = -19/2

2x - 2y = 13

Add both equations from left to right:

-3x/2 + 2 = (-3x + 4x)/2 = x/2 Establish 2 as common denominator

2y - 2y = 0, -19/2 + 13 =( -19 + 26)/2 = 7/2 Establish 2 as common denominator

Therefore x/2 = 7/2 ; using cross multiplication: 2x = 14

Diving through by 2 gives you x = 7

Substitute x = 7 into second original equation to get:

2x - 2y = 13 = 2(7) - 2y = 13

Simplify to get:

14 - 2y = 13 Subtract 14 from both sides of equation to get:

-2y = -1 = y=1/2. Final Answer: x = 7 and y = 1/2