Question

Решите систему линейных уравнений методом СЛОЖЕНИЯ! Подробно: 3x+2y=8 2x+6y=10

Answer 1

$\left \{ {{3x+2y=8} \atop {2x+6y=10}} \right. \left \{ {{5x+8y=18} \atop {x=5-3y}} \right. \left \{ {{5(5-3y)+8y=18} \atop {x=5-3y}} \right. \left \{ {{25-7y=18} \atop {x=5-3y}} \right. \left \{ {{7y=7} \atop {x=5-3y}} \right. \left \{ {{y=1} \atop {x=2}} \right.$

Answer 2

3x+2y=8

2x+6y=10

   

-9x-6y=-24

2x+6y=10

 

 

-7x=-14

x=2

 

2*2+6y=10

 

4+6y=10 6y=6 y=1   Ответ:(2;1)    

Answer 3

Solving the System of Linear Equations using the Method of Addition

To solve the system of linear equations using the method of addition, we'll follow these steps:

Step 1: Write down the given system of equations: - Equation 1: 3x + 2y = 8 - Equation 2: 2x + 6y = 10

Step 2: Multiply one or both equations by a constant to make the coefficients of either x or y the same (or additive inverses).

In this case, we can multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of x in both equations the same: - Equation 1 (multiplied by 3): 9x + 6y = 24 - Equation 2 (multiplied by 2): 4x + 12y = 20

Step 3: Add the two equations together to eliminate x or y. - (9x + 6y) + (4x + 12y) = 24 + 20 - 13x + 18y = 44

Step 4: Solve the resulting equation for the remaining variable. - 13x + 18y = 44 - We can solve this equation for x or y by isolating one variable and expressing it in terms of the other variable.

Let's solve for x: - 13x = 44 - 18y - x = (44 - 18y) / 13

Step 5: Substitute the value of x (or y) into one of the original equations to solve for the other variable.

Let's substitute the value of x into Equation 1: - 3x + 2y = 8 - 3((44 - 18y) / 13) + 2y = 8

Simplifying the equation: - (132 - 54y) / 13 + 2y = 8 - 132 - 54y + 26y = 104 - -28y = -28 - y = 1

Step 6: Substitute the value of y into the expression we found for x to find its value: - x = (44 - 18y) / 13 - x = (44 - 18(1)) / 13 - x = 26 / 13 - x = 2

Therefore, the solution to the given system of linear equations is x = 2 and y = 1.

Note: The solution to a system of linear equations represents the values of x and y that satisfy both equations simultaneously.

Let me know if you need any further assistance!