Question

Solve for a and b:

12a + 13b = 38 ; 4a + 11b = 17​

Answer 1

Answer:

Step-by-step explanation:

a)

Solving for a :

]12a + 13b = 38

Subtract 13b from both sides.

12a=38−13b

Divide both sides by 12.

12a /12 =  38−13b /12

Dividing by 12 undoes the multiplication by 12.

a=  38−13b/12

Divide 38−13b by 12.

a = -13b/12 + 19/6

Solving for b :

12a+13b=38

Subtract 12a from both sides.

13b=38−12a

Divide both sides by 13.

13b/13 = 38-12a/13

 

Dividing by 13 undoes the multiplication by 13.

b=  38−12a /13

b)

Solving for b :

4a+11b=17

Subtract 11b from both sides.

4a=17−11b

Divide both sides by 4.

4a/4 = 11b-17/4

 

Dividing by 4 undoes the multiplication by 4.

a = 11b-17/4

Solving for b :

4a+11b=17

Subtract 4a from both sides.

11b = 17-4a

Divide both sides by 11

11b/11 = 17-4a/11

Dividing by 11 undoes the multiplication by 11

b = 17-4a/11

Answer 2

a = 2.4625 and b = 0.65

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
• •  Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here, according to the given information, we are given that,

$12a+13b = 38...(1)$

And, $4a + 11b = 17...(2)$

Now, multiplying the equation 2 by 3, we get,

$12a+33b = 51...(3)$

Subtracting the equation 1 from equation 3, we get,

$(33-13)b=51-38$

Or, $20b=13.$

Or, $b =\frac{13}{20}=0.65$

Now, putting this value in equation 2, we get,

$4a = 17-11(\frac{13}{20} )$

Or, $a = 2.4625$

Hence, a = 2.4625 and b = 0.65

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