Question

7х-3у=-20 -4х-5у=-2​

Answer 1

7x-3y=20
7x-3y+20=-20+20
7x-3y+20=0

-4x-5y=-2
-4x-5y+2=0
4x+5y-2=0

Answer 2

To solve the system of linear equations, you can use either the substitution method or the elimination method. I'll demonstrate the elimination method here.

Given the system of equations:

1. $7x - 3y = -20$
2. $-4x - 5y = -2$

Let's start by multiplying both sides of the second equation by 7 to make the coefficients of $x$ in both equations equal. This will help us eliminate $x$ by adding the equations together.

Multiply the second equation by 7: $7(-4x) - 7(5y) = 7(-2)$ $-28x - 35y = -14$

Now we have:

1. $7x - 3y = -20$
2. $-28x - 35y = -14$

Now, let's add the two equations to eliminate $x$: $7x - 3y + (-28x) - 35y = -20 + (-14)$ $-21x - 38y = -34$

Now, solve the resulting equation for $y$: $-38y = -34 + 21x$ $y = \frac{34 - 21x}{38}$

Substitute the value of $y$ back into the first equation to solve for $x$: $7x - 3 \left( \frac{34 - 21x}{38} \right) = -20$

Simplify the equation: $7x - \frac{102 - 63x}{38} = -20$ $7x - \frac{102}{38} + \frac{63x}{38} = -20$ $7x + \frac{63x}{38} - \frac{102}{38} = -20$ $\frac{281x}{38} = -20 + \frac{102}{38}$ $\frac{281x}{38} = -\frac{760}{38}$

Now solve for $x$: $281x = -760$ $x = -\frac{760}{281}$

Now that we have the value of $x$, we can substitute it back into the equation for $y$: $y = \frac{34 - 21 \left( -\frac{760}{281} \right)}{38}$

Calculate $y$: $y = \frac{34 + \frac{15960}{281}}{38}$ $y = \frac{\frac{9568}{281}}{38}$ $y = \frac{9568}{10678}$

So, the solution to the system of equations is approximately: $x \approx -2.702$ $y \approx 0.896$