To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

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

-4a + y = -5
y = -5 + 4a

then substitute the result (-5 - -4a) into the second equation:

7a + 9(-5 + 4a) = 8
7a + (9 x -5) + (9 x 4a) = 8
7a - 45 + 36a = 8
7a + 36a = 8 + 45
43a = 53
a = \( \frac{53}{43} \)
a = 1\(\frac{10}{43}\)

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 3. 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, 4) and (2, 2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -\(\frac{1}{2}\)x + 3

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

8a - 9a = -1a

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

z² + 18z + 68 = z - 4
z² + 18z + 68 + 4 = z
z² + 18z - z + 72 = 0
z² + 17z + 72 = 0

Next, factor the quadratic equation:

z² + 17z + 72 = 0
(z + 8)(z + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 8) or (z + 9) must equal zero:

If (z + 8) = 0, z must equal -8
If (z + 9) = 0, z must equal -9

So the solution is that z = -8 or -9