How do you solve the system $2x - 15y = 33$ and $-3x + 4y = - 5$ ?

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Answer 1 · 2015-06-28T01:58:53

$x = -171/111$ and $y = -89/37$

(1) $2x-15y=33$
(2) $-3x+4y=-5$

Let's eliminate the $x$ variable.

Multiply Equation (1) by 3 and Equation (2) by 2. This gives

(3) $6x-45y=99$
(4) $-6x+8y=-10$

Add Equations (3) and (4).

(5) $-37y = 89$

(6) $y = -89/37$

Substitute (6) in (2).

$-3x+4y= -3x + 4(-89/37) = -3x – 356/37 = -5$

$-3x = 356/37 -5 = (356-185)/37 = 171/37$

$x = -171/111$

Check: Substitute in (2).

$-3x +4y = -3(-171/111) +4(-89/37) = 513/111 -356/37 = (37×513-111× 356)/(111×37) = (18981-39516)/4107 = -20535/4107 = 5$

How do you solve the system 2x - 15y = 332x - 15y = 33 and -3x + 4y = - 5-3x + 4y = - 5?