# How do you solve the following linear system:  8x - 7y = -3 , 6x - 5y = -1 ?

Mar 7, 2016

$\left(4 , 5\right)$

#### Explanation:

In order to solve systems of linear equations, we can use either of the three methods (1) elimination, (2) substitution, and (3) graphing. For this question I would use the elimination because I am more used to it and I think that it is quicker to do but note that using any of the three methods would give you the same result.

[Solution]
$8 x - 7 y = - 3$
$6 x - 5 y = - 1$

Multiplying the first equation by 3 and multiplying the second equation by 4 would make the coefficients of the first terms of both equations 24. This would allow us to eliminate the $x$ variable so we can solve for the $y$.

$24 x - 21 y = - 9$
$24 x - 20 y = - 4$

Subtracting the two equations...

$- y = - 5$
$y = 5$

Once we get the value of $y$ we would then substitute it to any of the two equations to solve for $x$. In this case, I would use the second equation since it has a smaller coefficient hence would produce smaller values.

$6 x - 5 y = - 1$
$6 x - 5 \left(5\right) = - 1$
$6 x - 25 = - 1$
$6 x = - 1 + 25$
$6 x = 24$
$x = 4$

$\left(4 , 5\right)$

[Checking byt substituting $\left(4 , 5\right)$]
$8 x - 7 y = - 3$
$6 x - 5 y = - 1$

*First Equation
$8 \left(4\right) - 7 \left(5\right) = - 3$
$32 - 35 = - 3$
$- 3 = - 3$

*Second Equation
$6 x - 5 y = - 1$
$6 \left(4\right) - 5 \left(5\right) = - 1$
$24 - 25 = - 1$
$- 1 = - 1$

Since both equations were satisfied by the computed values, we know that our answer is correct!