Question

4х + Зу = 8, 5х – у = -9.

Answer 1

$\left \{ {{4x+3y=8} \atop {5x-y=-9}} \right.$

Домножим выражение 5x-y=-9 на три

Получим

$\left \{ {{4x+3y=8} \atop {15x-3y=-27}} \right.$

Решим систему методом сложения

4x+3y+(15x-3y)=8+(-27)

4x+3y+15x-3y=8-27

19x=-19

x=-1

Мы получили икс, теперь легко найти игрек. Просто нужно подставить икс в одно из выражений системы.

Возьмём 5x-y=-9

y=5x+9=5*(-1)+9=-5+9=4

y=4

$\left \{ {{x=-1} \atop {y=4}} \right.$

Ответ: (-1; 4)

Answer 2

You've provided a system of two linear equations with two variables, x and y:

1. 4x + 3y = 8
2. 5x - y = -9

To solve this system of equations, you can use either the substitution method or the elimination method. I'll show you how to solve it using the elimination method:

First, we'll multiply equation (2) by 3 to make the coefficients of y in both equations cancel each other when summed:

1. 4x + 3y = 8
2. 15x - 3y = -27

Now, add equation (1) and equation (2) together:

(4x + 3y) + (15x - 3y) = 8 - 27

Combine like terms:

19x = -19

Now, divide both sides by 19 to solve for x:

x = -19 / 19 x = -1

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use equation (2):

5x - y = -9 5(-1) - y = -9 -5 - y = -9

Add 5 to both sides:

-y = -9 + 5 -y = -4

Now, multiply both sides by -1 to solve for y:

y = 4

So, the solution to the system of equations is x = -1 and y = 4.