Question

2x+3y=8 5x-3y=-1 способом додаваня

Answer 1

1) 2x+3y=8

+

5x-3y= -1

2)

2x+5x+3y+(-3y)=8+(-1)

7x=7|÷7

x=1

3y=8-2x

3y=8-2

3y=6

y=2

ответ (1;2)

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination), you can add the two equations together to eliminate one variable. Here's how:

Given the equations:

1. 2x + 3y = 8
2. 5x - 3y = -1

Step 1: Add the equations By adding the left sides and the right sides of the two equations, we can eliminate the variable 'y'.

(2x + 3y) + (5x - 3y) = (8) + (-1)

Simplifying the equation gives us: 2x + 5x + 3y - 3y = 8 - 1 7x + 0 = 7x = 7

Step 2: Solve for 'x' Divide both sides of the equation by 7 to isolate 'x':

7x/7 = 7/7 x = 1

Step 3: Substitute the value of 'x' back into one of the original equations to solve for 'y'. Let's use Equation 1:

2(1) + 3y = 8 2 + 3y = 8 3y = 8 - 2 3y = 6 y = 6/3 y = 2

Step 4: Check the solution To verify the solution, substitute the values of 'x' and 'y' into the second equation:

5(1) - 3(2) = -1 5 - 6 = -1 -1 = -1

Both sides are equal, which means the solution (x = 1, y = 2) satisfies both equations.

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