Question

Solve the following system of equations using the substitution method

5x+3y=1
X+2y=3

Answer 1

x= -1

y= 2

Explanation:

Answer 2

(x, y) = (-1, 2)

Explanation:

Substitution is easier if you already have an expression for the variable you want to make a substitution for. Here, we don't have that, but we have an equation with x having a coefficient of 1. We can use that to write an expression for x:

x = 3 -2y . . . . . subtract 2y from both sides of the second equation

5(3 -2y) +3y = 1 . . . . substitute for x in the first equation

15 -10y +3y = 1 . . . . . eliminate parentheses

-7y = -14 . . . . . . . . . . subtract 15, collect terms

y = 2 . . . . . . . . . . . . . divide by -7

Use this value in the equation for x:

x = 3 -2(2) = -1

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