Question

Solve the system of equations

x + 3y = 5
-x + 6y = 4

A) x = 1, y = 2
B) x = 2, y = 1
C) x = 1, y = 1
D) x = 0, y = 2

Answer 1

B) x=2, y=1

Explanation:

x+3y=5

-x+6y=4

solve the equation

x=5-3y

-x+6y=4

substitute the value of x into an equation

-1(5-3y)+6y=4

multiply numbers in parenthesis by -1

-5-3y+6y=4

put -5 as positive and add 5 to 4 and put -3y as positive and add to 6y.

9y=9

divide both sides by 9

y=1

substitute the value of y into an equation

x=5-3•1

multiply 3 to 1

x= 5-3

subtract 5 to 3

x=2

------------

x=2

y=1

------------

Answer 2

B) x = 2, y = 1

Explanation:

Add the two equations to eliminate the x-variable.

(x +3y) +(-x +6y) = (5) +(4)

9y = 9 . . . . . . .simplify

y = 1 . . . . . . . . divide by 9

You can substitute this value into either equation to find x.

x + 3(1) = 5

x = 2 . . . . . . . . subtract 3

The solution is (x, y) = (2, 1).