Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

# Solve the system by elimination?

{3a+4b=9

{-3a-2b=-3

Relevance
• 3a+4b=9------(1)

-3a-2b=-3-----(2)

(1)+(2)=>

2b=6=>

b=3

(1)+2*(2)=>

-3a=3=>

a=-1

a=-1

b=3

• First add the two equations to eliminate the variable "a."

3a + 4b = 9

-3a-2b =-3

----------------

2b = 6

b=3

Now, substitute the value of "b' into either equation.

3a + 4(3) = 9

3a = 9-12    (Subtract 4(3) = 12 from both sides of the equation.)

3a = -3

a= -1

Answer (a, b) = ( -1, 3)

• Subtract the two equations. This will eliminate 'a'

Hence

2b = 6

b = 3

When b = 3

3a + 4(3) = 9

3a + 12 = 9

3a = -3

a = -1

•  3a+4b =  9...(1).;

-3a-2b = -3...(2).;

(1)--->3a=9-4b;

Substitute (9-4b) for the 3a in (2) getting -(9-4b)-2b = -3;

ie., 9-4b+2b=3;

ie., 9-2b=3;

ie., 2b=9-3 = 6;

ie., b = 3;

Then (1)---> 3a = 9-12 = -3;

ie., a = -1.;

• (1) : 3a + 4b = 9

(2) : - 3a - 2b = - 3

You calculate (1) + (2)

(3a + 4b) + (- 3a - 2b) = 9 + (- 3)

3a + 4b - 3a - 2b = 9 - 3

2b = 6

→ b = 3

Recall (1) : 3a + 4b = 9

3a = 9 - 4b → where: b = 3

3a = - 3

→ a = - 1

• 3A+4B=9, 3A+2B=3

subtract>>0A+2B=6, B=3, A=-1

• 3a + 4b = 9

-3a - 2b = -3

2b = 6

b = 3

a = -1

• Anonymous
4 weeks ago

Surprising how many people get their education on Yahoo! Answers. Could be why the world is so screwed up nowadays.If you can't cook, get out of the kitchen. • {3a+4b=9 ... eq1

{-3a-2b=-3 .. eq2

----------------

2b = 6

solving for a from eq1

3a  + 4b = 9

3a + 4(3) = 9

3a + 12 = 9

3a = 9 - 12

3a = - 3

2b = 6, so b = 6/2 = 3

Multiply the second equation by 2:

-6a - 4b = -6

Add that to the first equation:

-3a = 3

a = 3/(-3) = -1