Question

2x+3y=10 x-2y=-9 подробно

Answer 1

Ответ в приложенном файле

Answer 2

Ответ: x=-1; y=4;

Объяснение: это система? Если да, то:

{2x+3y=10

{x-2y=-9

Решаем методом подстановки. Мы видим в нижнем уравнении x с коэф. 1, поэтому берём его за основу ⇒

x=-9+2y. После того как выразили x, подставляем его в первое уравнение вместо x ⇒

2*(-9+2y)+3y=10

-18+4y+3y=10

7y=28

y=28/7

y=4

Теперь подставляем в уравнение 4 заместо y.

2x+4*3=10

2x+12=10

2x=-2

x=-1

Сверяем со вторым уравнением.

-1-8=-9 . Подходит.

Answer 3

To solve the system of equations:

2x + 3y = 10 ...(Equation 1) x - 2y = -9 ...(Equation 2)

There are several methods to solve a system of equations, such as substitution, elimination, or matrix methods. I will demonstrate how to solve this system using the substitution method:

Step 1: Solve one equation for one variable in terms of the other variable. Let's solve Equation 2 for x: x = 2y - 9

Step 2: Substitute the expression for x from Step 1 into Equation 1. Replace x in Equation 1 with 2y - 9: 2(2y - 9) + 3y = 10

Step 3: Simplify and solve the resulting equation. Expand and simplify: 4y - 18 + 3y = 10 7y - 18 = 10

Step 4: Solve for y. Add 18 to both sides: 7y = 10 + 18 7y = 28

Divide both sides by 7: y = 28 / 7 y = 4

Step 5: Substitute the value of y back into one of the original equations to solve for x. Let's substitute y = 4 into Equation 2: x - 2(4) = -9 x - 8 = -9

Add 8 to both sides: x = -9 + 8 x = -1

Step 6: Check the solution. Substitute the values of x = -1 and y = 4 into both original equations to verify if they satisfy the equations.

Equation 1: 2x + 3y = 10 2(-1) + 3(4) = 10 -2 + 12 = 10 10 = 10 (True)

Equation 2: x - 2y = -9 (-1) - 2(4) = -9 -1 - 8 = -9 -9 = -9 (True)

Therefore, the solution to the system of equations is x = -1 and y = 4.