Question

What is the solution (x,y) to the system of equations below x + 9y = 3 y= 1/3 x + 7

Answer 1

Let's solve this by substitution.

y is given by the 2nd eqn as y = (1/3)x + 7. Subst. (1/3)x + 7 into the first eqn as a replacement for y: x + 9( (1/3)x + 7) = 3.

clear out fractions by mult. all 3 terms by 3: 3x + 9x + 63 = 3

Combine like terms: 12x = -60. Then x = -5

Find y by subst. -5 for x in the 2nd equation: y = (1/3)(-5) + 7

= -5/3 + 35/3 = 30/3 = 10.

Thus, the solution (x,y) of this system is (-5,10).