Question

3x – 2y = 17 –2x – 5y = 14 Solve using Elimination Please show work

Answer 1

Answer:

The solution is x=3 , y=-4 or (3,-4)

Step-by-step explanation:

Given equations (1 and 2) are:

$3x- 2y = 17\\-2x -5y = 14$

To solve a system of equation with elimination method, the co-efficients of one of the variables has to be equated and then the equations are added or subtracted to get an equation in one variable.

Multiplying equation 1 by 2:

$2(3x-2y) = 2*17\\6x-4y = 34\ \ \ \ \ Eqn\ 3$

Multiplying equation 2 by 3

$3(-2x-5y) = 3*14\\-6x-15y = 42\ \ \ \ Eqn\ 4$

Adding equation 3 and 4

$(6x-4y) + (-6x-15y) = 34+42\\6x-4y-6x-15y = 76\\-19y = 76\\\frac{-19y}{-19} = \frac{76}{-19}\\y = -4$

Putting y = -4 in equation 1

$3x-2(-4) = 17\\3x+8 = 17\\3x = 17-8\\3x = 9\\\frac{3x}{3} = \frac{9}{3}\\x = 3$

Hence,

The solution is x=3 , y=-4 or (3,-4)