System of Equations

Question

2x − 3y = −14

3x − 2y = −6

If (x, y) is a solution to the system of equations above, what is the value of x−y ?

Answer 1

To solve a question like this, we want to make either the x terms or the y terms match up to each other. Here's an example matching up the x terms:

2x − 3y = −14

3x − 2y = −6

To make the 2x in the top equation match the 3x in the bottom equation, multiply the entire top equation by 1.5:

1.5 * (2x - 3y) = 1.5 * (-14)

3x - 4.5y = -21

Now we have two equations that have 3x. Lastly, subtract the entire bottom equation from the top equation to be able to cancel out the 3x terms:

3x - 4.5y = -21

- (3x - 2y = -6)

-----------------------

-2.5y = -15

y = 6

Now that we've found the value of y, we can plug in its value of 6 in for y in either of the original functions given in the problem. I'll plug it into the first one:

2x − 3y = −14

2x - 3(6) = -14

2x - 18 = -14

2x = 4

x = 2

Now that we know the values of x and y, we can solve the original question: what is x-y?

x - y = ?

2 - 6 = -4

Answer: -4

Answer 2

Answer 3

Step 1: We can do this using elimination or substitution. Let’s use elimination, and let’s eliminate x. To do so, figure out what the LCM of 2 and 3 is.  

2: 2, 4, 6, 8 

3: 3, 6, 9, 12 

The LCM of 2 and 3 is 6.  

Step 2: Multiply both equations by a constant such that both coefficients of x are the LCM (6). The top equation must be multiplied by 3, and the bottom by 2, to achieve this.  

3 (2x − 3y = −14)    6x - 9y = - 42

2 (3x − 2y = −6)     6x - 4y = -12

Step 3: Take your two resulting equations and subtract them to eliminate x. Solve the result for y. 

   6x - 9y = - 42

-  6x - 4y = -12

   0x - 5y = -30 

   y = 6

Step 4: Substitute y back into either original equation. 

2x - 3 (6) = -14 

2x - 18 = -14

2x = 4

  X = 2 



Step 5: Do x - y. 

2 - 6 = -4

Answer 4

One approach is elimination. So, you start by multiplying the second equation by 2/3, giving you 2x- (4/3)y = -4. Then, subtract it from the first equation. So, variable by variable, you are doing 2x-2x = 0x, -3y-(-4/3)y, and -14-(-4). This leaves you with one equation that has just one unknown variable: (-5/3)y = -10. Then, you can solve this to get y=6. Plugging y=6 into either of the other equations allows you to solve for x, and you should get 2. Hope this helps! Let me know if you have any followup questions, and if you'd like math tutoring, please reach out to me! I am new to Wyzant, but I have 7+ years of tutoring experience others.

Answer 5

2x − 3y = −14

3x − 2y = −6

3x − 4.5y = −21 <-- Multiply top equation by 1.5 to help eliminate x

3x − 2y = −6

-2.5y = -15

y = 6

3x-2y = -6

3x-2(6) = -6

3x-12 = -6

3x = 6

x = 2

Therefore, x-y = 2-6 = -4

Hope this helped!