9x+2y=9 & -3x+y=2 . How would you arrange this?

Question

9x+2y=9

-3x+y=2

 

What does x and y equal?

Answer 1

We have a system of two equations and two variables (unknowns).

 

Eq 1)   9x + 2y = 9

Eq 2)   -3x + y =  2

 

We can solve this using substitution or elimination.

 

Let's use substitution first.

Since Eq 2 has a variable with a coefficient of 1, let's solve for that variable.

Eq 2) -3x + y = 2

We'll solve for y and call it Eq 3).

Eq 3)  y = 3x + 2

 

Now let's substitute Eq 3) into Eq 1)

Eq 1) 9x + 2y = 9

9x + 2(3x+2) = 9

And we can solve this for x

9x + 6x + 4 = 9

15x = 5

x = 1/3

 

Use this value of X in Eq 3) and solve for y.  Actually you can use any of the equations above.

y = 3(1/3) + 2

y = 3

So x = 1/3 and y = 3

 

The other method is the elimination method.

Eq 1) 9x + 2y = 9
Eq 2) -3x + y = 2

 

Notice that Eq 1 has a 9x and a 2y

Also Eq 2 has a -3x and a y.

 

We need to make the coefficients for the x or the y equal.  The easiest way to do this for this set of equations is to multiply Eq 2) by 2.  We'll call the new equation Eq 5)

 

Eq 1) 9x + 2y = 9
Eq 2) -3x + y = 2

 

Eq 5)   2( -3x + y = 2) ==> -6x + 2y = 4

 

Let's put these two equations together.

 

Eq 1)    9x + 2y = 9

Eq 5)  -6x + 2y = 4

 

We can now subtract Eq 5 from Eq 1

 

15x = 5

x = 1/3

Use x=1/3 in Eq 1)

9 (1/3) + 2y = 9

3 + 2y = 9

2y = 6

y = 3

 

Hope this helps.

Answer 2

Use the substitution method.  We can substitute the second equation into the first equation.  From the second equation,

 

y = 3x + 2

 

 

Now the first equation becomes

 

9x + 2(3x + 2) = 9

 

Solve for x from this new version of the first equation.  Once you have your x value, substitute it into the second equation to solve for y.

Answer 3

Hi Sunshine,

 

Your question involves solving systems of equation. One way of solving it is as follows:

9x+2y=9
-3x+y=2

 

Multiplying the second equation by 3, we have

 

9x+2y=9
-9x+3y=6

 

Adding the two equations, we have,

 

5y=15

y= 3.

 

To solve for x, plug in 3 in place of y in one of the equations.

 

9x+2y=9

9x+2(3) = 9

9x = 9-6

9x = 3

x = 1/3.

 

Therefore, x= 1/3, y=3

 

I hope this helps.

A