Busy. Please wait.
Log in with Clever

show password
Forgot Password?

Don't have an account?  Sign up 
Sign up using Clever

Username is available taken
show password

Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.
Your email address is only used to allow you to reset your password. See our Privacy Policy and Terms of Service.

Already a StudyStack user? Log In

Reset Password
Enter the associated with your account, and we'll email you a link to reset your password.
Didn't know it?
click below
Knew it?
click below
Don't Know
Remaining cards (0)
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

  Normal Size     Small Size show me how

Module 5 - Linear Eq

Math 113 Online: Module 5 - Linear Equations and Substitution Method

Determine whether each ordered pair is a solution of the system of linear equations. {x+y=8 and 3x+4y=29 a) (2,6) b) (3,5) Plug in each ordered pair into both equations to determine if said ordered pairs are solutions to the linear equations. 2+6=9; 3(2)+4(6)=29/6+24=30 and 3+5=8; 3(3)+4(5)=29/9+20=29. Ordered pair a isn't a solution, but pair b is.
Solve the System of linear equations by graphing. {x+y=9 and x-y=5 Once you've graphed both equations, find the point at which both lines intersect. The ordered pair should satisfy the equations. The solution of the system is (7,2) because it completes both linear equations. 7+2=9;7-2=5
Without​ graphing, decide. a) Are the graphs of the equations identical​ lines, parallel​ lines, or lines intersecting at a single​ point? and b) How many solutions does the system​ have? {9x+7=27 and x+8y=8 Rewrite both equations in slope intercept form y=-9+27 and y=-1/8x+1. Identify the slopes and y-intercepts for both lines. The slopes for the lines are -9 and -1/8. The slopes are different, and must intersect at one point; meaning one solution.
Solve the system of equations using the substitution method. {x+y=10 and x=4y The first step is to solve one of the equations for one variable. The second equation; x=4y has already been solved for x, so we'll use it. 4y+y=10 (Combine like terms) 5y=10; y=2 x=4(2); x=8. So the solution is (8,2)
Solve the system of equations by the substitution method. {y=5x+7 and y=7x+8 Substitute 5x+7 for y in the 2 equation. 5x+7=7x+8 isolate the x terms on the left side by subtracting 7x and adding 7. -2x=1; x=-1/2 Plug in x for the 1st equation. y=5(-1/2)+7; y=-5/2+7. Simplify. y=9/2 So the ordered pair is (-1/2,9/2)
Solve the system of equations by the substitution method. {12x+3y=8 and -4x=y+8 Neither equation is solved for x or y, so we'll isolate y on the right side of equation 2. -4x-8=y Now fill in the 1st equation 12x+3(-4x-8)=8 Use the distributive property on the left side. 12x-12x-24=8 -24=8 is a false statement/no solution.
Solve the system of equations by the substitution method. {4x-y=3 and 5x-2y=12 Neither is solved, so we'll isolate y in the 1st equation. -y=3-4x Solve for y y=4x-3 Now substitute y in the 2nd equation. 5x-2(4x-3)=12 Distributive property. 5x-8x+6=12; -3x+6=12, isolate x. -3x=6, solve for x, x=-2. Replace x in the first equation.
Solve the system of equations by the substitution method. {4x-y=3 and 5x-2y=12 (Continued) y=4(-2)-3, y=-8-3, y=-11. So the ordered pair is (-2,-11)
Solve the system of equations by the substitution method. {3x+12y=15 and 4x+18y=22 Neither is solved, so we'll isolate x in the 1st equation. 3x=15-12y, solve for x. x=5-4y, now substitute x in the 2nd equation. 4(5-4y)+18y=22 Distribute. 20-16y+18y=22, combine like terms. 20+2y=22 isolate y on the left side. 2y=2; y=1
Solve the system of equations by the substitution method. {3x+12y=15 and 4x+18y=22 (Continued) Replace y in the first equation. x=5-4(1) Solve. x=1 So the ordered pair is (1,1)
Created by: 1118006241566176
Popular Math sets




Use these flashcards to help memorize information. Look at the large card and try to recall what is on the other side. Then click the card to flip it. If you knew the answer, click the green Know box. Otherwise, click the red Don't know box.

When you've placed seven or more cards in the Don't know box, click "retry" to try those cards again.

If you've accidentally put the card in the wrong box, just click on the card to take it out of the box.

You can also use your keyboard to move the cards as follows:

If you are logged in to your account, this website will remember which cards you know and don't know so that they are in the same box the next time you log in.

When you need a break, try one of the other activities listed below the flashcards like Matching, Snowman, or Hungry Bug. Although it may feel like you're playing a game, your brain is still making more connections with the information to help you out.

To see how well you know the information, try the Quiz or Test activity.

Pass complete!
"Know" box contains:
Time elapsed:
restart all cards