Slove the following system of equations
2x-7y=-7
-5x+6y=-17

x = 7

y = 3

Step-by-step explanation:

We are given two equations

2x - 7y = -7 eqn 1

-5x + 6y= -17 eqn 2

Let's pick eqn 1, to make y the subject of the formula

2x - 7y = -7

2x + 7 = 7y

Divide both sides by 7, to make y the subject of the formula

(2x + 7) / 7 = 7y/7

(2x + 7) / 7 = y

Substitute y into the equation 2

-5x + 6y = -17

-5x + 6(2x + 7)/7 = -17

Open the bracket

-5x + (12x + 42) / 7 = -17

LCM = 7

(-35x + 12x + 42) / 7 = -17

(-23x + 42)/7 = -17

Cross multiply

-23x + 42 = -17 * 7

-23x + 42 = -119

-23x = -119 - 42

-23x = -161

- cancels -

23x = 161

Divide both sides by 23 to get the value of x

23x / 23 = 161/23

x = 161/23

x = 7

Substitute the value of x into eqn 1

2x - 7y = -7

2(7) - 7y = -7

14 - 7y = -7

- 7y = -7 - 14

-7y = -21

Divide both sides by -7 to get the value of y

-7y/ -7 = -21/-7

Well, - cancels -

y = -21/-7

y = 3

The values are

x = 7

y = 3

We can verify our values

Let's take eqn 2 to confirm

-5x + 6y = -17

x = 7

y = 3

= -5(7) + 6(3)

= -35 + 18

= -17

Our values are correct

4x and 6y

im not sure though