Answer
The solution to this system of equations is $x = -\frac{5}{48}$ and $y= -\frac{3}{16}$.
Work Step by Step
When we use elimination to solve a system of equations, we need to make sure that one of the variables in both equations is the same but differing only in sign.
Let's take a look at the system of equations in this exercise. In this case, we already have one variable term in both equations that is the same value but with opposite signs:
$-3x + 7y = -1$
$3x + 9y = -2$
Let's add the two equations:
$16y = -3$
Divide each side by $16$ to solve for $y$:
$y= -\frac{3}{16}$
Substitute this value for $y$ into one of the equations to solve for $x$:
$3x + 9(-\frac{3}{16}) = -2$
Multiply first:
$3x - \frac{27}{16} = -2$
Collect constant terms on the right side of the equation:
$3x = -\frac{32}{16} + \frac{27}{16}$
Add the terms on the right side of the equation:
$3x = -\frac{5}{16}$
Divide each side by $3$ to solve for $x$:
$x = -\frac{5}{48}$
The solution to this system of equations is $x = -\frac{5}{48}$ and $y= -\frac{3}{16}$.
To see if this solution is correct, substitute in the values we just found for $x$ and $y$ into one of the original equations:
$-3(-\frac{5}{48}) + 7(-\frac{3}{16}) = -1$
Multiply first:
$\frac{5}{16} - \frac{21}{16} = -1$
Subtract:
$-1 = -1$
The two sides are equal; therefore, this solution is correct.
This system of equations is consistent because it has at least one solution. It is also independent because there is only one solution.
