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

$\\ \sf\longmapsto 11x=27$

$\\ \sf\longmapsto x=\dfrac{27}{11}$

Now

Put in eq(1)

$\\ \sf\longmapsto 3\dfrac{27}{11}+3y=6$

$\\ \sf\longmapsto \dfrac{81}{11}+3y=6$

$\\ \sf\longmapsto 3y=6-\dfrac{81}{11}$

$\\ \sf\longmapsto 3y=\dfrac{66-81}{11}$

$\\ \sf\longmapsto 3y=\dfrac{15}{11}$

$\\ \sf\longmapsto y=\dfrac{15}{33}$

Answer 2

Answer:

• (-3, 5)

Step-by-step 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