Question

8) [7x-11y=23, 21x+2y=-1;​

Answer 1

$\begin{cases} 7x-11y=23\ \ | \cdot (-3) \\ 21x+2y=-1 \end{cases}\\\\\begin{cases} -21x+33y=-69 \\ 21x+2y=-1 \end{cases}\\+--------\\35y=-70\ \ |:35\\ y=-2\\\\7x-11y=2\\ 7x-11*(-2)=23\\7x+22=23\\7x=23-22\\7x=1\ \ |:7\\x=\frac{1}{7}\\\\\begin{cases}x=\frac{1}{7}\\ y=-2 \end{cases}$

Answer 2

To solve this system of linear equations:

1. 7x - 11y = 23
2. 21x + 2y = -1

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

First, multiply both sides of equation (1) by 3 to make the coefficients of y in both equations equal:

1. 21x - 33y = 69

Now, you have the following system of equations:

1. 21x - 33y = 69
2. 21x + 2y = -1

Subtract equation (2) from equation (1) to eliminate x:

(21x - 33y) - (21x + 2y) = 69 - (-1)

Now, simplify:

21x - 33y - 21x - 2y = 69 + 1

The x terms cancel out, and you're left with:

-35y = 70

Now, divide both sides by -35 to solve for y:

-35y / -35 = 70 / -35

y = -2

Now that you have the value of y, you can substitute it back into either of the original equations to solve for x. Let's use equation (1):

7x - 11(-2) = 23

7x + 22 = 23

Subtract 22 from both sides:

7x = 23 - 22

7x = 1

Now, divide both sides by 7 to solve for x:

7x / 7 = 1 / 7

x = 1/7

So, the solution to the system of equations is:

x = 1/7 y = -2