Question

2x + 3y = 5,2x – 4y = -9.​

Answer 1

$-\left \{ {{2x+3y=5} \atop {2x-4y=-9}} \right.\\ ------\\7y=14\\\\y=2\\\\2x=5-3y=5-3*2=5-6=-1\\\\x=-0,5\\\\Otvet:\boxed{(-0,5 \ ; \ 2)}$

Answer 2

To solve this system of linear equations:

1. 2x + 3y = 5
2. 2x - 4y = -9

You can use the method of elimination or substitution. I'll demonstrate how to solve it using the elimination method:

Step 1: Multiply both sides of equation (1) by 2 to make the coefficients of x in both equations the same:

1. 4x + 6y = 10

Now you have:

1. 4x + 6y = 10
2. 2x - 4y = -9

Step 2: Multiply both sides of equation (2) by 2 to make the coefficients of x in both equations the same:

1. 4x + 6y = 10
2. 4x - 8y = -18

Step 3: Now, subtract equation (2) from equation (1) to eliminate x:

(4x + 6y) - (4x - 8y) = 10 - (-18)

This simplifies to:

4x + 6y - 4x + 8y = 10 + 18

Step 4: Combine like terms:

14y = 28

Step 5: Divide both sides by 14 to solve for y:

y = 28 / 14 y = 2

Now that you've found the value of y, you can substitute it back into one of the original equations to solve for x. I'll use equation (1):

2x + 3y = 5 2x + 3(2) = 5 2x + 6 = 5

Subtract 6 from both sides:

2x = 5 - 6 2x = -1

Now, divide both sides by 2 to solve for x:

x = -1 / 2 x = -0.5

So, the solution to the system of equations is x = -0.5 and y = 2.