Question

Consider the equations: y = 3x + 2 and y = 2x + 1.

Solve the system of equations by completing the table of values to find an ordered pair that satisfies both equations.

Answer 1

Explanation:

Given : Consider the equations
`y=3x+2` and
`y=2x+1`

To find : Solve the system of equations by completing the table of values to find an ordered pair that satisfies both equations ?

Solution :

For the equation,
`y=3x+2`

`y(-1)=3(-1)+2=-1`

`y(0)=3(0)+2=2`

`y(1)=3(1)+2=5`

`y(2)=3(2)+2=8`

`y(3)=3(3)+2=11`

We create a table,

x y

-1 -1

0 2

1 5

2 8

3 11

For the equation,
`y=2x+1`

`y(-1)=2(-1)+1=-1`

`y(0)=2(0)+1=1`

`y(1)=2(1)+1=3`

`y(2)=2(2)+1=5`

`y(3)=2(3)+1=7`

We create a table,

x y

-1 -1

0 1

1 3

2 5

3 7

Answer 2

(-1,-1)

Explanation:

• y = 3x + 2
• x y
• -1 -1
• 0 2
• 1 5
• 2 8
• 3 11

• y = 2x + 1
• x y
• -1 -1
• 0 1
• 1 3
• 2 5
• 3 7

Sample calculation

y = 3x + 2 y = 2x + 1

x = 2 x = 2

y = ? y = ?

y = 3*2 + 2 y = 2*2 + 1

y = 6 + 2 y = 4 + 1

y = 8 y = 5

The two that give exactly the same answer is

(-1, - 1)