Question

I need help with this math please​

Answer 1

We have the following system of equations,

$\begin{cases}-5x+6y=8 \\-5x+4y=2\end{cases}$

First multiply the first equation on both sides by -1 to get,

$\begin{cases}5x-6y=-8 \\-5x+4y=2\end{cases}$

Then add the equations to get,

$5x-5x-6y+4y=-8+2\implies-2y=-6 \\ \implies\boxed{y=3}$

Now just plug in the value of y into one of the original equations and solve for x (I'll pick the second one).

$-5x+4\cdot3=2\implies-5x=-10 \\ \implies\boxed{x=2}$.

So the final solution is a point where these two lines intersect and that is at $\boxed{(2,3)}$.

Hope this helps.

Answer 2

In order to solve using elimination, we need to be able to get rid of one variable, so that we can solve for the other. We need to subtract these two equations given from one another, or multiply the bottom equation by a negative and add them together.

(-5x + 6y = 8) - (-5x + 4y = 2)

(-5x + 6y = 8) + (5x - 4y = -2)

0x + 2y = 6

2y = 6

y = 3

Now that we know the value of one variable, we can take that value and plug it back into one of the original equations and solve for the value of the other variable.

-5x + 6y = 8

-5x + 6(3) = 8

-5x + 18 = 8

-5x = -10

x = 2

The solution to this system of equations is (2, 3).

Hope this helps!! :)