Question

Find a solution to the following system of equations –5x + 2y = 9 3x + 5y = 7

Answer 1

Answer: (-1, 2)

Explanation:

Let's start by solving for x in

`-5x+2y=9\\-5x+2y+-2y=9+-2y\\-5x=9+-2y\\(-5x)/(-5) =(9+-2y)/(-5) \\x=(2)/(5) y+(-9)/(5)`

We can now sub this value of x in 3x+5y=7 and solve

`3x+5y=7\\3((2)/(5) y+(-9)/(5))+5y=7\\(3)((2)/(5) y)+(3)((-9)/(5))+5y=7\\(6)/(5) y+(-27)/(5)+5y=7\\(6)/(5) y+(25)/(5)y +(-27)/(5)=7\\(31)/(5) y+(-27)/(5)=7\\(31)/(5) y+(-27)/(5)+(27)/(5)=7+(27)/(5)\\(31)/(5) y=(62)/(5) \\((31)/(5) y)/((31)/(5)) =((62)/(5) )/((31)/(5)) \\y=2`

Now we can sub in 2 for y in one of the equations

`3x+5(2)=7\\3x+10=7\\3x+10-10=7-10\\3x=-3\\(3x)/(3) =(-3)/(3) \\x=-1`

x=-1 and y=2 giving us the point (-1, 2)