An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

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

-3a + y = 8
y = 8 + 3a

then substitute the result (8 - -3a) into the second equation:

2a - 7(8 + 3a) = -2
2a + (-7 x 8) + (-7 x 3a) = -2
2a - 56 - 21a = -2
2a - 21a = -2 + 56
-19a = 54
a = \( \frac{54}{-19} \)
a = -2\(\frac{16}{19}\)

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:

y² + 2y - 41 = -3y - 5
y² + 2y - 41 + 5 = -3y
y² + 2y + 3y - 36 = 0
y² + 5y - 36 = 0

Next, factor the quadratic equation:

y² + 5y - 36 = 0
(y - 4)(y + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 4) or (y + 9) must equal zero:

If (y - 4) = 0, y must equal 4
If (y + 9) = 0, y must equal -9

So the solution is that y = 4 or -9