Question

4x−3y=76x−2y=410x−11y=97x+3y=1015x−12y=36x+8y=1

Answer 1

4x-3y=7
4x=7+3y
x=7/4+3/4y

6x-2y=4
6x=4+2y
x=2/3+1/3y

10x-11y=9
10x=9+11y
x=9/10+11/10y

7x+3y=10
7x=10-3y
x=10/7-3/7y

15x-12y=3
15x=3+12y
x=1/5+4/5y

6x+8y=1
6x=1-8y
x=1/6-4/3y

Answer 2

It looks like you've provided a system of linear equations with multiple equations. To solve this system and find the values of x and y, you can use various methods such as substitution, elimination, or matrix methods. Since you've provided a set of five equations, I'll demonstrate how to solve this system using the elimination method.

Here's the system of equations:

1. $4x - 3y = 7$
2. $6x - 2y = 4$
3. $10x - 11y = 9$
4. $7x + 3y = 10$
5. $15x - 12y = 36$
6. $x + 8y = 1$

We can start by using the elimination method to eliminate one variable from two pairs of equations. Let's start with equations 1 and 2:

Equation 1: $4x - 3y = 7$ Equation 2: $6x - 2y = 4$

Let's multiply equation 2 by 3 so that the coefficients of $y$ match up:

$3 \cdot (6x - 2y) = 3 \cdot 4$ $18x - 6y = 12$

Now, let's subtract equation 1 from this new equation to eliminate $y$:

$(18x - 6y) - (4x - 3y) = 12 - 7$ $18x - 6y - 4x + 3y = 5$ $14x - 3y = 5$ ...(Equation A)

Next, let's work with equations 4 and 6:

Equation 4: $7x + 3y = 10$ Equation 6: $x + 8y = 1$

Let's multiply equation 6 by 7 and equation 4 by $−1$ so that the coefficients of $y$ match up:

$7 \cdot (x + 8y) = 7 \cdot 1$ $7x + 56y = 7$

$(-1) \cdot (7x + 3y) = (-1) \cdot 10$ $-7x - 3y = -10$

Now, let's add these two equations to eliminate $y$:

$(7x + 56y) + (-7x - 3y) = 7 - 10$ $7x + 56y - 7x - 3y = -3$ $53y = -3$ $y = -\frac{3}{53}$ ...(Equation B)

Now that we have the value of $y$, we can substitute it into Equation A to solve for $x$:

$14x - 3 \left(-\frac{3}{53}\right) = 5$ $14x + \frac{9}{53} = 5$ $14x = 5 - \frac{9}{53}$ $x = \frac{5 \cdot 53 - 9}{53 \cdot 14}$ $x = \frac{265 - 9}{742}$ $x = \frac{256}{742}$ $x = \frac{128}{371}$

So, the solution to the system of equations is: $x = \frac{128}{371}$ and $y = -\frac{3}{53}$.