The problem is to solve the given system of linear equations: $2x + 7y = 22$ (1) $5x + 8y = 17$ (2) And then describe the system of equations.

1. Problem Description

The problem is to solve the given system of linear equations:

$2x + 7y = 22$ (1)

$5x + 8y = 17$ (2)

And then describe the system of equations.

2. Solution Steps

We can solve the system of equations using either substitution or elimination. Let's use elimination. Multiply equation (1) by 5 and equation (2) by 2 to eliminate $x$.

$5(2x + 7y) = 5(22) \implies 10x + 35y = 110$ (3)

$2(5x + 8y) = 2(17) \implies 10x + 16y = 34$ (4)

Subtract equation (4) from equation (3):

$(10x + 35y) - (10x + 16y) = 110 - 34$

$19y = 76$

$y = \frac{76}{19} = 4$

Substitute $y = 4$ into equation (1):

$2x + 7(4) = 22$

$2x + 28 = 22$

$2x = 22 - 28$

$2x = -6$

$x = -3$

So the solution is $x = -3$ and $y = 4$. The solution to the system is $(-3, 4)$.

The system is independent and consistent because the two lines intersect at one point.

3. Final Answer

The solution to the system is (-3, 4).

The equations are independent and consistent. Their graphs intersect at one point.