11 is the sum of twice a number and three times a second number. The second number is equal to the difference of two and the dust number. Find the two numbers

Question

Using two variables, write and solve a system of equation for each word problem. 

Answer 1

Hi Leah.

 

x = first number

y = second number

 

From the first sentence

11 = 2x + 3y

 

From the second sentence (I'm assuming the word "dust" should be "first"

y = 2-x

rewritten as 

x + y = 2

 

So your system of equations is

2x + 3y = 11

 x  +  y  =  2

 

Multiply the 2nd equation by -2

2x + 3y = 11

-2x - 2y = -4

 

Add the two equations together

y = 7

 

Use y=7 to solve for x

x = 2-y = 2-7 = -5