Question

Система 5x-2y=-19 4x+y=-10

Answer 1

$\left \{ {{5x-2y=-19} \atop {4x+y=-10}} \right.$

$\left \{ {{y=-10-4x} \atop {5x-2*(-10-4x)=-19}} \right.$

$\left \{ {{5x+20+8x=-19} \atop {y=-10-4x}} \right.$

$\left \{ {{13x=-39} \atop {y=-10-4x}} \right.$$\left \{ {{x=-3} \atop {y=-10+12}} \right.$

Значит x=-3, y=2

Ответ:(3;2)

Answer 2

To solve the system of equations:

1. 5x - 2y = -19
2. 4x + y = -10

There are multiple methods to solve this system, such as substitution, elimination, or matrix methods. Let's use the elimination method to solve these equations.

Step 1: Multiply both sides of Equation 1 by 2 to make the coefficients of y in both equations the same. This will allow us to eliminate y when we add the two equations together.

1. 2 * (5x - 2y) = 2 * (-19) 10x - 4y = -38

Step 2: Now, add the modified Equation 1 to Equation 2:

(10x - 4y) + (4x + y) = -38 + (-10)

Step 3: Simplify the equation:

10x - 4y + 4x + y = -48

Step 4: Combine like terms:

14x - 3y = -48

Now we have a new equation:

3. 14x - 3y = -48

Step 5: To eliminate y from the equation, multiply both sides of Equation 2 by 3, and add it to Equation 3:

3 * (4x + y) = 3 * (-10) 12x + 3y = -30

(14x - 3y) + (12x + 3y) = -48 + (-30)

Step 6: Simplify and combine like terms:

26x = -78

Step 7: Solve for x:

x = -78 / 26 x = -3

Step 8: Now that we have the value of x, we can find the value of y by substituting x back into either Equation 1 or Equation 2. Let's use Equation 2:

4x + y = -10 4 * (-3) + y = -10 -12 + y = -10

Step 9: Solve for y:

y = -10 + 12 y = 2

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