total of $ 33 comma 000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $ 4 comma 000 comma how much will be invested in each type of investment?

the amount invested in bonds $18500

the amount invested in certificates of deposits is $14500

Step-by-step explanation:

Let x represent the amount invested in bonds.

Let y represent the amount invested in certificates of deposits.

A total of $33000 is to be invested, some in bonds and some in certificates of deposit (CDs). This would be expressed as

x + y = 33000 - - - - - - - - - - - 1

If the amount invested in bonds is to exceed that in CDs by $4000, this would be expressed as

x = y + 4000

Substituting x = y + 4000 into equation 1, it becomes

y + 4000 + y = 33000

2y + 4000 = 33000

2y = 33000 - 4000

2y = 29000

y = 29000/2 = 14500

x = y + 4000 = 14500 + 4000

x = 18500

x = -2

y = -4

Step-by-step explanation:

After adding both equations, you would then have

0 + 11y = -44

11y = -44

y = -44/11

y = - 4

Now, you substitute for y in either of the first equations. I'm using the second one.

-3x + 2(-4) = -2

-3x - 8 = -2

-3x = -2 + 8

-3x = 6

x = -6/3

x = -2

Therefore, x = -2 and y = -4

You can test for it by substituting both in the equation

-3(-2) + 2(-4) =

6 - 8 = -2