You need to find the value of a so solve the first equation in terms of z:

4a + z = -9
z = -9 - 4a

then substitute the result (-9 - 4a) into the second equation:

-9a + 6(-9 - 4a) = 5
-9a + (6 x -9) + (6 x -4a) = 5
-9a - 54 - 24a = 5
-9a - 24a = 5 + 54
-33a = 59
a = \( \frac{59}{-33} \)
a = -1\(\frac{26}{33}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

4b + 5 < \( \frac{b}{-9} \)
-9 x (4b + 5) < b
(-9 x 4b) + (-9 x 5) < b
-36b - 45 < b
-36b - 45 - b < 0
-36b - b < 45
-37b < 45
b < \( \frac{45}{-37} \)
b < -1\(\frac{8}{37}\)

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 0) and (2, 2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = \(\frac{1}{2}\)x + 1

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 9² + 3²
c² = 81 + 9
c² = 90
c = \( \sqrt{90} \)

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.