Algebra Skills:

Slope and y-intercept form: y = mx +b

Standard form: ax +by +c = 0

Rules:

1. X must lead and be positive

2. No fraction

Graphing Strategies using standard forms (the x and y intercepts):

ax +by =C

Y-intercept is when x is zero

X-intercept is when y is zero

Find the two intercepts on the graph, join them.

1. Don’t use this strategy if the intercepts are going to be fractions, because it won’t be accurate, use y=mx+b

Writing Equations of Lines (using delta y delta x strategy)

2. Find slope first

3. m = ∆y/∆x (by substituting one pair of points)

Solving Equations with Rational Coefficients

Use scalar

Solve Linear System (using the method of substitution 1)

y = 3x −4 (expression for y),

Substitute into x +y = 8

x+3x-4=8

Solve Linear System (using the method of substitution 2)
y1 = ax+b
y2 = cx+d

y1=y2
ax+b = cx+d

Solve Linear System (using the method of elimination)
ax+y=c
dx+y=e (subtraction)
gx+y =o (y is eliminated to get x)

Tip: addition is always better than subtraction)

Real Life Word problems

A vending machine contains a total of 395 quarters and dimes. The total value of the coins is $66.80. How many of each coin are required to make this amount?

q + d = 395 0.25q + 0.10d = 66.80

A chemistry student was asked to make 25mL of 48% alcohol by volume by mixing 40% alcohol solution by volume and 60% alcohol solution by volume. How many litres of each alcohol solution must the student use to make 25mL of 48% alcohol?

a40 + a60 = 25 0.40a40 + 0.60a60 = 0.48(25)

A store owner sells peanuts of $4.80/kg and raisins for $2.40/kg. She will make a mixture of peanuts and raisins called Nutsins and sell it for $3.36/kg. How many kilograms of peanuts and raisins does she need to make 200kg of Nutsins?

r+ p = 200 4.80p + 2.40r = 3.36(200)

The length of a rectangle is 19 m longer than its width. If the perimeter is 606 m, what are the dimensions of the rectangle?

l = w + 19 2l + 2w = 606

When 4 times the larger of two numbers is added to 3 times the smaller the result is 68. Seven times the larger number less 5 times the smaller number is 37. What are the numbers?

4l + 3s = 68 7l −5s = 37

	Created by sandersbay over 12 years ago

Math Note on Linear System Skills, created by sandersbay on 26/02/2014.