How do you solve the system of linear equations 5x - 4y = 6 and 2x + 3y = 2?

1 Answer
Dec 6, 2017

x= 26/23 and y = -2/23

Explanation:

5x - 4y = 6 --------------- Let this be equation (1).

2x + 3y = 2 --------------Let this be equation (2).

To eliminate one variable, we must make the coefficient of that variable same in both the equations. Say, if we want to eliminate y in order to find x,

Multiply equation(1) by 3 and multiply equation(2) by 4, we get the following set:

(1) x 3 => 15x - 12y = 18 -----------(1')and

(2) x 4 => 8x +12y =8--------------(2'),

We see that the coefficients of y are equal and opposite in sign, so we add these two equations(1') and(2'), in order to eliminate y:

=> 15x+8x -cancel(12y)+cancel(12y) =18+8

=> 23x =26

=> x= 26/23= 1 3/23

Substituting value of x in any one equation, say in (1),

=> 5x - 4y = 6

=> 5 xx 26/23 -4y = 6

=> 130/23 -4y =6

=> -4y = 6-130/23

=> -4y = 6(23/23) - 130/23= (138-130)/23

=> y = 1/-4 xx 8/23

=> y = 1/-cancel4^1 xx cancel8^2/23

=> y =-2/23

So we have, x= 26/23 and y = -2/23

Let us cross check by substituting values of x and y in equation (2),

2x + 3y = 2

=> Left hand side = 2(26/23) + 3(-2/23)

= 52/23 - 6/23 = 46/23 = 2= Right hand side = 2
Hence values obtained are correct.