More on equations are located in Chapter 8
- Simulataneous Equations
- ax² = c
- Point of Intersection
- Similar to an equation
- Always give answer in terms of the pronumeral.
- When dividing by a negative, reverse the inequality sign
4 - 5x < 1 -5 x < -3 5x > 3 # we divide by -1, and reverse the inequality sign accordingly x > ⅗
- Open circle for
>(greater than) and
<(less than). For example:
x > 1= x is greater than 1
- Closed circle for
≥(greater than or equal to) and
≤(less than or equal to). For example:
x ≤ 1= x is less than or equal to 1
- Representing sets on a number line (e.g
-2 < x ≤ 3) can be done like this:
The arrow on the number line points the same direction as the sign
it makes me want to eliminate… eliminate YOU!
You can solve simultaneous equations in different ways, graphically, using substitution, and using elimination. We will only cover substitution and elimination here.
Substitute one equation into the other, and solve.
y = 2x - 4  4x - y = 6  Sub  ->  4x - (2x - 4) = 6 4x - 2x + 4 = 6 2x + 4 = 6 2x = 2 x = 1
You can add or subtract equations together to eliminate pronumerals.
- Decide whether you should add or subtract.
- If you can’t add or subtract, multiply the equations to get a common pronumeral (similar to fractions)
- Eliminate the pronumeral and solve
3x - y = 4  5x + y = 4  # add the equations together 3x + 5x + (-y) + y = 8 8x = 8 Therefore, x = 1
What if it isn’t possible to eliminate a pronumeral in the equations’ current form?
7x - 2y = 3  4x - 5y = 6  # multiply  by 4 and  by 7 28x - 8y = 12  28x - 35y = -42  #  -  -8y - 35y = 12 - (-42) -43y = 54
ais the coefficient;
xis the base; and
cis the product.
x² = 25
∴ x = ±√25 # surd form ∴ x = ±5 # basic numeral
The point where two lines intersect each other