Answer
Our solution is:
$$(2, 2)$$
Work Step by Step
To solve a system of equations by the addition method, you have to transform the equations so that the coefficients of one of the variables for both equations differ only in sign. In this problem, we want to work with the $x$ variable. We will transform the second equation.
We multiply the second equation by $-2$ to get:
$$-2(4x + 5y) = -2(22)$$
We distribute to get:
$$-8x - 10y = -44$$
We now put the two equations together to add them:
$$ 8x - 4y = 16$$
$$-8x - 10y = -44$$
We add them to get the following equation:
$$-14y = -28$$
Divide by $-14$ to solve for $y$:
$$y = 2$$
We can now plug in what we got for $y$ into one of the equations to get $x$:
$$4x + 7(2) = 22$$
Multiply, according to order of operations:
$$4x + 14 = 22$$
Subtract $7$ from each side to isolate the $x$ term:
$$4x = 8$$
Solve for $x$ by dividing by $4$ on both sides:
$$x = 2$$
Our solution is:
$$(2, 2)$$
