Solving Using Elimination
Solve using Elimination:
-12x + 5y = 2
14x - 5y = -4
(-1,-2)
Which method should you use to solve the following system of equations?
y = 4x + 10
3x + 2y = 9
Substitution
Assign variables for the following scenario: The theater club sells a total of 101 tickets to its first play. A student ticket costs $1. An adult ticket costs $2.50. Total ticket sales are $164.
x + y = 101, x + 2.50y = 164
(let x=... let y=...)
let x = # of student tickets
let y = # of adult tickets
4x + 10y = 12
-8x - 2y = 14
Multiply the _______ equation by ____ in order to eliminate x.
Multiply the _FIRST_ equation by _2_ in order to eliminate x.
Is (1, -7) a solution to the following system of equations?
-4x - 4y = 24
7x + 3y = -18
No, it is only a solution to the first equation.
Solve using elimination:
2x + 10y = 20
3x + 10y = 30
(10,0)
Eliminate x to solve for y:
2x + 3y = 12
x - 5y = -7
y=2
Write a system of equations for the following scenario: You open 2 bank accounts on the same day. In your checking account, you initially deposit $150 and add $50 each week. In your savings account, you initially deposit $500 and add $100 each week.
checking account:
y = 50x + 150
savings account:
y = 100x + 500
Add the first equation TO THE SECOND EQUATION. Rewrite the resulting system:
5x + 7y = -12
-4x - 7y = 14
5x + 7y = -12
x = 2
isolate y in the following equation: (y = ....)
6x + 2y = 14
y = -3x + 7
or
y = 7 - 3x
Solve using elimination:
x + 8y = 2
3x + 4y = 26
(10,-1)
Which method would be easier to solve the following system of equations?
6x + 2y = 12
4x + 4y = 16
Elimination
Write a system of equations to represent the following scenario:
Washing 4 cars and 3 trucks takes 130 minutes. Washing 2 cars and 5 trucks takes 190 minutes.
4c + 3t = 130
2c + 5t = 190
Multiply the first equation by -3 then add the result to the SECOND equation. What will the resulting system be?
2x - 4y = 8
6x + 2y = 10
2x - 4y = 8
14y = -14
Solve the following system of equations using substitution.
y = 9x + 2
y = 3x - 4
(-1,-7)
Solve using elimination:
5x + y = 9
10x - 7y = -18
(1,4)
Complete the first steps of substitution to solve for y
2x + 4y = 16
x = 2y - 4
y = 3
Write a system of equations for the following scenario, then solve: A concessions stand sold a total of 138 small and large popcorns. A small popcorn costs $2.50, and a large popcorn costs $4.00. Total popcorn sales were $466.50. How many bags of each size of popcorn were sold? Let x= # of small popcorns sold, let y= # of large popcorns sold
x + y = 138
2.5x + 4y = 466.5
(57, 81)
John multiples the second equation by .25 then adds it TO THE FIRST EQUATION, what is his resulting system?
.25x + .5y = 6
x + y = 16
.25y = 2
x + y = 16
solve using the method of your choice
6x - 7y = -20
4x + 5y = 6
(-1,2)
Solve using elimination:
-5x + 7y = -7
-2x - 2y = 2
(0,-1)
Use elimination or substitution to solve the following system of equations
2x + 5y = 19
y - 3x = -3
(2,3)
Write a system of equations and solve using your chosen method:
A hot dog stand sells hot dogs for $4.50 and chips for $2.50. On Monday, the stand sold 15 items and made $45.50. The stand only sold hot dogs and chips. How many hot dogs and chips did they sell?
h + c = 15
4.5h + 2.5c = 45.5
h = 4, c = 11
Gwen multiplies the first equation by -3, and the second equation by 2. She then adds the new first equation TO THE NEW SECOND EQUATION. What is her resulting system?
2x + 5y = 2
3x + 7y = 4
2x + 5y = 2
-y = 2
Solve using the method of your choice:
10x + 10y = 2
4x + 4y = 4
no solution