Question

Решите систему уравнений методом сложения 4x+7y=18 6x+11y=10 ;

Answer 1

$\displaystyle\bf\\\left \{ {{4x+7y=18} \ |\cdot(-3)\atop {6x+11y=10} \ |\cdot 2} \right. \\\\\\+\left \{ {{-12x-21y=-54} \atop {12x+22y=20}} \right. \\------------\\y=-34\\\\4x=18-7y=18-7\cdot(-34)=18+238=256\\\\x=256:4=64\\\\Otvet:(64 \ ; \ -34)$

Answer 2

Solving the System of Equations using the Method of Addition

To solve the system of equations using the method of addition, we will add the two equations together to eliminate one of the variables. Let's solve the system of equations:

Equation 1: 4x + 7y = 18 Equation 2: 6x + 11y = 10

To eliminate the variable "x," we can multiply Equation 1 by 6 and Equation 2 by 4. This will make the coefficients of "x" in both equations equal:

6 * (4x + 7y) = 6 * 18 4 * (6x + 11y) = 4 * 10

Simplifying these equations, we get:

24x + 42y = 108 24x + 44y = 40

Now, subtracting Equation 1 from Equation 2, we can eliminate "x":

(24x + 44y) - (24x + 42y) = 40 - 108

Simplifying further, we have:

2y = -68

Dividing both sides of the equation by 2, we find:

y = -34

Now, substitute the value of "y" back into either Equation 1 or Equation 2 to solve for "x." Let's use Equation 1:

4x + 7(-34) = 18

Simplifying, we get:

4x - 238 = 18

Adding 238 to both sides of the equation, we have:

4x = 256

Dividing both sides of the equation by 4, we find:

x = 64

Therefore, the solution to the system of equations is x = 64 and y = -34.

Note: The solution to the system of equations is x = 64 and y = -34.