Question

Решите систему (2-мя способами 1.способ подстановки и 2.способ алгебраического сложения) x-2y=-1 3x+4y=17 плиз. заранее спасибо.

Answer 1

Не резко, но прочитать можно

Answer 2

Solution using Substitution Method:

To solve the system of equations using the substitution method, we will solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for x:

Equation 1: x - 2y = -1

Solving for x, we get:

x = 2y - 1

Now, substitute this value of x into the second equation:

Equation 2: 3x + 4y = 17

Substituting x = 2y - 1, we get:

3(2y - 1) + 4y = 17

Simplifying the equation:

6y - 3 + 4y = 17 10y - 3 = 17 10y = 20 y = 2

Now, substitute the value of y back into the first equation to find x:

x - 2(2) = -1 x - 4 = -1 x = 3

Therefore, the solution to the system of equations is x = 3 and y = 2.

Solution using Algebraic Addition Method:

To solve the system of equations using the algebraic addition method, we will add the two equations together in a way that eliminates one variable.

Let's add the two equations:

Equation 1: x - 2y = -1 Equation 2: 3x + 4y = 17

Adding the equations:

(x - 2y) + (3x + 4y) = -1 + 17

Simplifying the equation:

4x + 2y = 16

Now, we have a new equation with only x and y. Let's solve this equation:

4x + 2y = 16

Divide the equation by 2 to simplify:

2x + y = 8

Now, we have a new equation:

2x + y = 8

We can solve this equation for y:

y = 8 - 2x

Now, substitute this value of y into the first equation:

x - 2(8 - 2x) = -1

Simplifying the equation:

x - 16 + 4x = -1 5x - 16 = -1 5x = 15 x = 3

Now, substitute the value of x back into the equation y = 8 - 2x to find y:

y = 8 - 2(3) y = 8 - 6 y = 2

Therefore, the solution to the system of equations is x = 3 and y = 2.

Please let me know if you need any further assistance!