Question

Z−3b=52z−4b=35  решит систему способом агебр. сложением​

Answer 1

Ответ: z=42.5

b=12.5

Объяснение:1) умножаем первое уравнение на -2 (выйдет -2z +6b=-10)

2)плюсуем эти два уравнения

(Получим 2b=25, значит b=12.5)

3) подставляем значение b в первое уравнение системы:

z-37.5=5;

z= 42.5

Answer 2

To solve the system of equations using the method of algebraic addition (also known as the method of elimination), we need to eliminate one of the variables from one of the equations by adding the two equations together. Here's the step-by-step process:

Given the system of equations:

1. Z - 3b = 52
2. z - 4b = 35

Step 1: Rearrange the equations, if necessary, so that the coefficients of one of the variables are the same or additive inverses.

The coefficients of 'z' in the two equations are 1 and 1, which are already the same. So, we don't need to perform any rearrangement.

Step 2: Add the equations together to eliminate one of the variables.

(Z - 3b) + (z - 4b) = 52 + 35

Now, add the 'z' terms together and the '-3b' and '-4b' terms together:

Z + z - 3b - 4b = 87

Step 3: Simplify the equation.

2z - 7b = 87

Now, we have a new equation with only one variable, 'z', which we can solve for.

Step 4: Solve for 'z'.

2z = 87 + 7b

z = (87 + 7b) / 2

Step 5: Substitute the value of 'z' back into one of the original equations to solve for 'b'.

Using equation 1:

Z - 3b = 52

(87 + 7b) / 2 - 3b = 52

Step 6: Solve for 'b'.

Multiply both sides by 2 to eliminate the fraction:

87 + 7b - 6b = 104

Subtract 87 from both sides:

7b - 6b = 104 - 87

b = 17

Step 7: Substitute the value of 'b' back into the equation to solve for 'z'.

z = (87 + 7b) / 2

z = (87 + 7 * 17) / 2

z = (87 + 119) / 2

z = 206 / 2

z = 103

So, the solution to the system of equations is: z = 103 b = 17