Question

Solve the system of equations using the addition method 2a+3b=-1 ; 3a+5b=-2

Answer 1

Answer:

a = 1 and b= -1

Step-by-step explanation:

It is given two equations,

2a + 3b = -1  and

3a + 5b = -2  

To find the solution of given equations

Let, 2a + 3b = -1   ----(1)

3a + 5b = -2   ------(2)

(1) * -3 ⇒

-6a - 9b = 3    ----(3)

(2) * 2 ⇒

6a + 10b = -4   -----(4)

(3) + (4 )⇒

-6a - 9b = 3    ----(3)

6a + 10b = -4   -----(4)

  0 + b  = -1

(1) ⇒ 2a + 3b = -1  

2a + (3 * -1) = -1

2a = -1 + 3 = 2

a = 2/2 =1

Therefore, a = 1 and b = -1

Answer 2

Answer:

Then, a=-1 and b=-1

Step-by-step explanation:

We need to solve the following system of equations using the adition method:

2a+3b=-1       (i)

3a+5b=-2      (ii)

First, we multiply the equation (i) by -3 and the equation (ii) by 2, so we get:

-6a-9b=3

6a+10b=-4

Adding the two equations we have:

-6a-9b=3

6a+10b=-4

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

 0  + b = -1

Then b=-1. Now, let's substitute the value of b into equation (i):

2a+3b=-1

2a + 3(-1) = -1

2a -3 = -1

2a = 2

a = 1

Then, a=-1 and b=-1