How do you solve x= 3y-1 and x+2y=9 using substitution?

3 Answers
Mar 6, 2018

(5,2)

Explanation:

You know the value of the variable x, so you can substitute that into the equation.
overbrace((3y - 1))^(x) + 2y = 9

Remove the parentheses and solve.
3y - 1 + 2y = 9

=> 5y - 1 = 9

=> 5y = 10

=> y = 2

Plug y into either equation to find x.
x = 3overbrace((2))^(y) - 1

=> x = 6 - 1

=> x = 5

(x,y) => (5,2)

Mar 6, 2018

x=5, y=2

Explanation:

Given x=3y-1 and x+2y=9

Substitute x=3y-1 into x+2y=9,

(3y-1)+2y=9
5y-1=9
5y=10
y=2

Substitute y=2 into the first equation,
x=3(2)-1
x=5

Mar 6, 2018

x = 5
y = 2

Explanation:

If

x = 3y -1

then use that equation in the second equation. This means that

(3y - 1) + 2y = 9

5y - 1 = 9

5y - 1 + 1 = 9 + 1

5y = 10

(5y)/5 = 10/5

y = 2

Having said this, just replace the y in the first equation in order to get the x.

x = 3(2) -1

x = 6 -1

x = 5

After that, just check that the values make sense:

x = 3y - 1

5 = 3(2) -1

5 = 6 - 1

5 = 5

And for the second one:

x + 2y = 9

5 + 2(2) = 9

5 + 4 = 9

9 = 9

Both answers satisfy both equations, which makes them correct.