Question

X + 2y = 73y - 5x = 4​

Answer 1

Ответ:

$\left \{ {{x+2y=7} \atop {3y-5x=4}} \right.$

$\left \{ {{x+2y=7 | *5} \atop {3y-5x=4}} \right.$

5x+10y+3y-5x=35+4

13y=39

y = $\frac{39}{13}$

y = 3

x+2*3=7

x+6=7

x=7-6

x = 1

Ответ: (1; 3)

Пошаговое объяснение:

Answer 2

To solve the system of equations:

1. X + 2y = 7
2. 3y - 5x = 4

You can use the method of substitution or elimination. Let's use the elimination method in this case:

First, we'll multiply the first equation by 5 and the second equation by 2 to make it easier to eliminate one of the variables:

1. 5(x + 2y) = 5(7)
2. 2(3y - 5x) = 2(4)

This simplifies the equations to:

1. 5x + 10y = 35
2. 6y - 10x = 8

Now, we can add the two equations together to eliminate x:

(5x + 10y) + (6y - 10x) = 35 + 8

Combine like terms:

5x - 10x + 10y + 6y = 43

Simplify:

-5x + 16y = 43

Now, you have a single equation with one variable:

-5x + 16y = 43

Next, isolate one of the variables, for example, y:

16y = 5x + 43

Now, divide both sides by 16 to solve for y:

y = (5x + 43)/16

Now that you have an expression for y, you can substitute it into either of the original equations to solve for x. Let's use the first equation:

X + 2y = 7

Substitute the expression for y:

X + 2((5x + 43)/16) = 7

Now, solve for x:

X + (10x + 86)/16 = 7

To clear the fraction, you can multiply both sides of the equation by 16:

16X + 10x + 86 = 112

Combine like terms:

26x + 86 = 112

Subtract 86 from both sides:

26x = 112 - 86

26x = 26

Now, divide by 26 to find the value of x:

x = 26/26

x = 1

So, the solution to the system of equations is:

x = 1 y = (5x + 43)/16 = (5(1) + 43)/16 = 48/16 = 3