Question

Solve the System and write the solution as an ordered pair.

3x+3y=6
5x-6y=15

Answer 1

`\\ \sf\longmapsto 3x+3y=6\dots(1)`

`\\ \sf\longmapsto 5x-6y=15\dots(2)`

Multiply eq(1) by 2 and eq(2) by 1

`\\ \sf\longmapsto 6x+6y=12`

`\\ \sf\longmapsto 5x-6y=15`

• Add

`\\ \sf\longmapsto 11x=27`

`\\ \sf\longmapsto x=(27)/(11)`

Now

Put in eq(1)

`\\ \sf\longmapsto 3(27)/(11)+3y=6`

`\\ \sf\longmapsto (81)/(11)+3y=6`

`\\ \sf\longmapsto 3y=6-(81)/(11)`

`\\ \sf\longmapsto 3y=(66-81)/(11)`

`\\ \sf\longmapsto 3y=(15)/(11)`

`\\ \sf\longmapsto y=(15)/(33)`

Answer 2

• (-3, 5)

Explanation:

Given system:

• 3x+3y=6
• 5x-6y=15

Simplify the first equation by dividing all terms by 3:

• 3x/3 + 3y/3 = 6/3
• x + y = 2
• x = 2 - y

Substitute x into the second equation:

• 5(2 - y) + 6y = 15
• 10 - 5y + 6y = 15
• y = 15 - 10
• y = 5

Find x:

• x = 2 - 5
• x = -3