Question

MAX POINTS!!! Write and solve a system of equations. Be sure to label the variables. The difference of two numbers is two. Two times the first number plus the second number is thirteen. What are the numbers? Show and explain all work.

Answer 1

Let the numbers be a and b

• a-b=2--(1)
• 2a+b=13---(2)

Adding both

`\\ \sf\longmapsto 3a=15`

`\\ \sf\longmapsto a=5`

Putting in eq(1)

`\\ \sf\longmapsto 5-b=2`

`\\ \sf\longmapsto b=5-2`

`\\ \sf\longmapsto b=3`

Answer 2

• 5 and 3

Explanation:

Let the numbers be x and y.

The equations are:

• x - y = 2
• 2x + y = 13

Add up the equations to eliminate y and solve for x:

• x - y + 2x + y = 2 + 13
• 3x = 15
• x = 15/3
• x = 5

Now find the value of y:

• y = x - 2
• y = 5 - 2
• y = 3