Question

Решите систему уравнений способом cложения:

Answer 1

$\left \{ {{3x-5y=23|*(-2)} \atop {2x+3y=9|*3}} \right. \\\left \{ {{-6x+10y=-46} \atop {6x+9y=27}} \right. +\\-6x+6x+10y+9y=-46+27;19y=-19\Rghtarrow y=-1\\3x-5y=23;3x+5=23;3x=18\Rightarrow x=6$

Ответ: (6;-1).

Answer 2

Solving the System of Equations by Addition

To solve the system of equations using the method of addition, we need to add the two equations together in a way that eliminates one of the variables. Let's solve the given system of equations:

Equation 1: 2x + 3y = 2 Equation 2: -2x + 5y = -18 To eliminate the x variable, we can multiply Equation 1 by 2 and Equation 2 by 2, and then add the resulting equations together:

2 * (2x + 3y) = 2 * 2 -2 * (-2x + 5y) = -2 * -18

This simplifies to:

4x + 6y = 4 4x - 10y = 36

Now, we can add the two equations together:

(4x + 6y) + (4x - 10y) = 4 + 36

This simplifies to:

8x - 4y = 40

Now we have a new equation:

Equation 3: 8x - 4y = 40

To solve for x, we can rearrange Equation 3:

8x = 4y + 40 x = (4y + 40) / 8 x = y/2 + 5

Now that we have the value of x in terms of y, we can substitute this expression into one of the original equations to solve for y. Let's substitute it into Equation 1:

2 * (y/2 + 5) + 3y = 2 y + 10 + 3y = 2 4y + 10 = 2 4y = -8 y = -2

Now that we have the value of y, we can substitute it back into the expression for x:

x = (-2)/2 + 5 x = -1 + 5 x = 4

Therefore, the solution to the system of equations is x = 4 and y = -2.

Please let me know if you need any further assistance!