How do you solve the following linear system: x + 2y = 13, 3x – y = 4 ?

1 Answer
Feb 21, 2016

color(blue)(x=3, y=5)

Explanation:

we can use,

-color(blue)(Substitution Method)

Solving,

color(red)(x+2y=13)
as equation(1)

color(red)(3x-y=4)
as equation(2)

first we must get the value of x in equation(1), using algebraic techniques (isolating the variable x), we get:

color(red)(x = 13-2y)
as equation(3)

substitute equation(3) to equation(2) to eliminate x,

3(13-2y)-y=4

39-6y-y=4 (Combine like terms to simplify)

39-7y=4

-7y = 4 - 39

-7y = -35

y = (-35)/-7

color(blue)(y = 5)

substitute y to either equation(1) or equation(2) to get the final value of variable x

Substituting y to Equation(1),

x+2y=13

x+2(5)=13

x+10=13

x=13-10

color(blue)(x=3)