solving system of linear equations

Question

Solve the system of linear equations:

Answer 1

Multiplies 1st equation by 4: x+y = 4

Multiplies 2nd equation by 35: 5x - 7y = 35

Solves first equation for y : y= 4-x

Substitutes : 5x - 7(4-x) = 35

5x - 28 + 7x = 35

12x - 28 = 35

12x = 63

x = 63/12 = 21/4

y = 4 - x = 4 - 21/4 = 16/4 - 21/4 = -5/4

CHECK:

(1/4)(21/4) + (1/4)(-5/4) = 21/16 - 5/16 = 16/16 = 1

(1/7)(21/4) - (1/5)(-5/4) = 3/4 + 1/4 = 1