Question

1) x + y = 10; 3х+у=17​

Answer 1

Ответ:

x + y = 10                                                                3x + y = 17

x + y - 10 = 10 - 10                                                   3x + y - 17 = 17 - 17

x + y - 10 = 0                                                            3x + y - 17 = 0

Пошаговое объяснение:

Answer 2

To solve this system of linear equations, we can use either the substitution method or the elimination method. I'll demonstrate both methods, and you can choose the one you prefer.

Let's start with the given system of equations:

1. x + y = 10
2. 3x + y = 17

Substitution Method:

Step 1: Solve one equation for one variable. Let's solve equation (1) for y:

x + y = 10 y = 10 - x

Step 2: Substitute the expression for y from step 1 into the other equation (equation 2) and solve for x:

3x + (10 - x) = 17 3x + 10 - x = 17 2x + 10 = 17 2x = 17 - 10 2x = 7 x = 7 / 2 x = 3.5

Step 3: Substitute the value of x into the expression for y (from step 1) to find the value of y:

y = 10 - x y = 10 - 3.5 y = 6.5

So, the solution to the system of equations is x = 3.5 and y = 6.5.

Elimination Method:

Step 1: Multiply one or both equations by appropriate constants to make the coefficients of one variable in both equations equal. Let's start by multiplying equation (1) by 3 to make the coefficients of y in both equations the same:

3 * (x + y) = 3 * 10 3x + 3y = 30

The modified system becomes:

1. 3x + 3y = 30
2. 3x + y = 17

Step 2: Subtract equation (2) from equation (1) to eliminate the variable y:

(3x + 3y) - (3x + y) = 30 - 17 2y = 13 y = 13 / 2 y = 6.5

Step 3: Substitute the value of y into equation (1) and solve for x:

x + y = 10 x + 6.5 = 10 x = 10 - 6.5 x = 3.5

Again, the solution is x = 3.5 and y = 6.5.

Both methods yield the same solution, and the solution to the given system of equations is x = 3.5 and y = 6.5.