Answer
The ordered pair $(3, 1)$ is the solution to this equation. This system of equations is consistent because it has at least one solution. It is also independent because there is only one solution.
Work Step by Step
The equation gives $y$ in terms of $x$, so let's use this expression for $y$ to substitute into the second equation:
$3x + (2x - 5) = 10$
Remove the parentheses, paying attention to the signs:
$3x + 2x - 5 = 10$
Combine like terms:
$5x - 5 = 10$
Collect constant terms on the right side of the equation:
$5x = 15$
Divide each side of the equation by $5$ to solve for $x$:
$x = 3$
Now that we have the value for $x$, we can substitute it into the first equation to find $y$:
$y = 2(3) - 5$
Multiply first:
$y = 6 - 5$
Subtract to solve for $y$:
$y = 1$
We got $(3, 1)$ as the solution
Let's check the answer by substituting both values into one equation to see if both sides are equal:
$1 = 2(3) - 5$
Multiply first:
$1 = 6 - 5$
Subtract:
$1 = 1$
The two sides equal one another; therefore, the ordered pair $(3, 1)$ is the solution to this equation. This system of equations is consistent because it has at least one
solution. It is also independent because there is only one solution.
