Question

Решите методом добавления: 4a + 6b = 9 3a - 5b = 2

Answer 1

Первое уравнение умножим на 3, а второе на 4

12a+18b=27
12a-20b=8

Отнимаем от первое второе

38b=19
b=19:38
b=1/2

12a-20*1/2=8
12a-10=8
12a=18
a=18:12
a=9/6
a=1,5

Answer 2

4a + 6b = 9/ *5⇒20a+30b=45
3a - 5b = 2/*6⇒18a-30b=12
прибавим
38a=57
a=57/38=1,5
6+6b=9
6b=3
b=0,5

Answer 3

To solve the system of equations using the method of addition (also known as the method of elimination or the method of substitution), we need to eliminate one variable by adding the two equations together. Here's how it works:

Given the equations:

1. 4a + 6b = 9
2. 3a - 5b = 2

Step 1: Choose a variable to eliminate. In this case, we'll eliminate the variable "b."

Step 2: Multiply the equations by suitable constants so that the coefficients of "b" will cancel out when added together. To do this, we need to make the coefficients of "b" in both equations equal, but with opposite signs. The least common multiple (LCM) of 6 and 5 is 30, so we'll use that.

Multiply equation (1) by 5 and equation (2) by 6: 5 * (4a + 6b) = 5 * 9 6 * (3a - 5b) = 6 * 2

Which becomes:

1. 20a + 30b = 45
2. 18a - 30b = 12

Step 3: Add the modified equations together to eliminate "b." (20a + 30b) + (18a - 30b) = 45 + 12 20a + 18a = 57 38a = 57

Step 4: Solve for "a": a = 57 / 38 a = 3/2 or 1.5

Step 5: Substitute the value of "a" back into one of the original equations to solve for "b." Let's use equation (1): 4a + 6b = 9 4 * (3/2) + 6b = 9 6 + 6b = 9

Step 6: Solve for "b": 6b = 9 - 6 6b = 3 b = 3/6 b = 1/2 or 0.5

So, the solution to the system of equations is: a = 1.5 and b = 0.5.