Substitute
y = 3x + 1
y = 6x + 10
x = -3 , y = -8
4x + 9y = 29
6x - 9y = 21
x = 5, y = 1
30 - 4y = 14
y = ?
y=4
The sum of two numbers is 45. The difference between the two numbers is 35. What are the numbers?
x +y += 45
x- y= 35
What are the two methods for solving simultaneous equations?
Elimination and substitution method
y = -2x + 13
y = 4x - 11
x = 4, y = 5
-2x + 4y = 8
x + 4y = 26
x = 6, y = 5
Transpose for b:
2xy+3b=5
b=(5-2xy)/3
A motorist buys 24 liters of gas and 5 liters of oil for $1070 from AID, while another motorist buys 18 liters of gas and 10 liters of oil for $1240, also from AID. Find the cost of 1 liter of gas and 1 liter of oil at AID.
24x +5y =1070
18x + 10y=1240
When using the elimination method, and after making your coefficients the same. If the signs are the same, will you add or subtract?
Subtract
4x + 2y = -20
y = x - 4
x = -2, y = -6
-8x - 5y = 18
8x + 7y = -22
x = -1, y = -2
Solve for y:
3+ (y-1)/2=15
y=25
What are the 6 steps to the elimination method?
1 -6 in order
When using the elimination method, and after making your coefficients the same. If the signs are different, will you add or subtract?
ADD
5x - y = 21
y = -7x + 15
x = 3, y = -6
5x - 4y = -8
-5x + 6y = 12
x = 0, y = 2
Find x if a=2 and b = -1
x=-1
A pigeon can lay either white or brown eggs. Three white eggs and two brown eggs weigh 13 ounces, while five white eggs and four brown eggs weigh 24 ounces. Find the weight of a brown egg and of a white egg.
3a + 2b = 13
5a +4b =24
What's the first step for solving simultaneous equations using the substitution method?
Make one of the variable in one of the equations the subject.
y = -8x - 3
8x + 4y = 12
x = -1, y = 5
-8x + 2y = 28
-8x - 7y = 10
x = -3, y = 2
If V= 2ab + abt2
Find b when V=-6, a = -1 and t = 2
b=1
Twice a number added to three times another gives 21. Find the numbers, if the difference between them is 3.
2x+3y=21
x-y=3
What are the two goals of solving a linear equations?
Answers may vary