Solving systems

Question

solve this system:

5x-2y=21

4x+2y=15

 

Solve this system: 

-3x+2y=12

y=2x+5

 

need to show all work 

Answer 1

The method for solving systems of two equations is to 1) express one of the variables (call it "a") in terms of the other (call it "b"), 2) use the expression obtained in (1) to get the numeric value of "a", and 3) Use the numeric value of "a" to get the value of "b."

 

Here goes:

 

5x-2y=21
4x+2y=15

 

First, we express y in terms of x using the second equation: y = 7.5 - 2x.

 

Next, we plug (7.5 - 2x) into the first expression in place of y, giving

 

5x - 2(7.5 - 2x) = 9x - 15 = 21

 

This expression implies that 9x = 36 and thus that x = 4. With the knowledge that x = 4, we can solve either of the two equations for y. Picking the second one, we have

 

16 + 2y = 15, 

 

which implies 1 = -2y, and therefore y = -1/2.

 

Taking up the second system, we can start directly with the second expression, y = 2x + 5. We substitute (2x + 5) for y in the top equation, giving

 

-3x + 2(2x + 5) = x + 10 = 12,

 

which reveals that x = 2. Now we can plug x = 2 into the second equation to get y = 2x + 5 = 9.

Answer 2

Solve the top system using linear combination by adding the two equations; solve for x, then substitute the found value for x into either equation to solve for y.

     5x  - 2y = 21
+   4x + 2y = 15

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

     9x         = 36            Notice the terms with y become 0y; divide both sides by 4 to find x.

       x         = 4

 

Now that you know that x is 4, substitute 4 for x into either equation, such as the first one

    5(4) - 2y = 21

    20   - 2y = 21

           - 2y = 1

               y = -1/2         check the answer (4, 1/2) in the second equation 

 

In the second system, the second equation says y = 2x + 5, so in the first equation wherever there is an y, substitute the y with (2x +5), and the solve for x. After you have a value for x, substitute the found value for x into either equation to solve for y.