1.03 Solve Systems of Three Linear Equations

Process started over with only now two equations step 3: solve equation

13y+2z=-24 / 6y-2z=-24 back to step 1: isolate a variable we will isolate 2z. 13y+2z=-24 -13y =-13y 2z=-14-13y we isolated 2z on to step 2: plug in your isolated variable into a equation. 6y-(-14-13y)=-24 distribute the negative into the parenthesis -*-14= positive 14 -*-13y= positive 13y 6y+14+3y=-24 combine liked terms 3y+6y=9y 9y+14=-24 isolate 9y 9y+14=-24 -14=-14 9y=-38 now isolate y by dividing 9 on both sides -38/9=-2 y=-2

What is the solution to the system of equations using the linear combination method? {5x+y=24 x+y=5 A.(−2, 12) B.(0, 2) C. (1, −8) D. (−3, 17)

A.(-2,12)

What is the solution to the system of equations? {2x−3y=−27 −3x+2y=23 A (7, −3) B(3, 11) C(−3, 7) D(−24, −7)

C(-3,7)

1.03 Quiz:Solve Systems of Linear Equations

Questions 1-5

system of three linear equations (in three variables)

This is three separate equations with 3 letter variables. for example: x-5y+z=16 , 2x+3y+4z=18 , x+y-z=-8

What are steps to solve three equations with three variable?

You want to use the substitution method for solving a triple equation, triple variable problem. Step 1: Isolate a variable Step 2 :substitute expression into both of the other equations and solve for one variable. Step 3: solve the equation step 4:substitute the value of one variable to find the value of the other variable. step 5: repeat step 4 as needed step 6:check your answers to make sure they are correct

What is the solution to the system of equations? {x+y=6 x=y+2 A. (2, 4) B. (3, 3) C. (6, 4) D. (4, 2)

liked explained above just plug-in answers to see if it makes a true statement. D.(4,2)

STEP 6: check work

plug in y=-2 z=6 and x=0 to all the equations equation number 1 x-5y+z=16 so to know the answers we found out about the variables are correct this part x-5y+z with the plug in variable needs to be = to 16. 0-5(-2)+6=16 -5(-2)=10 10+6=16 16=16 so the variables answers are correct for this equation. But don't settle just because it works for this one it might not work for the rest. 2(0)+3(-2)+4(6)=18 18=18 0+4-6=-8 -8=-8

Which ordered pair is the solution to the system of equations? x+3y=−12 y=1/3x−6 A.(10, −2 2/3) B. (−5, −2 1/3) C. (3, −5) D. (−9, −9)

simply just plug-in the answers into the equation given and see which one make it true. you be using the substitution method. Since y = 1/3x - 6, replace the y variable in the first equation with 1/3x - 6 and solve for x: ( https://tex.z-dn.net/?f=%20x%2B3%28%5Cfrac%7B1%7D%7B3%7Dx-6%29%3D-12%5C%5C%20x%2Bx-18%3D-12%5C%5C%202x-18%3D-12%5C%5C%202x%3D6%5C%5C%20x%3D3%20 ) <this link is the picture of the steps to find x. Now that we have the value of x, plug it into either equation to solve for y: ( https://tex.z-dn.net/?f=%203%2B3y%3D-12%5C%5C%203y%3D-15%5C%5C%20y%3D-5%5C%5C%20%5C%5C%20y%3D%5Cfrac%7B1%7D%7B3%7D%2A3-6%5C%5C%20y%3D1-6%5C%5C%20y%3D-5%20 )this link is the picture of the steps to find y. so after you seen steps in picture answer is C. (3,-5)

Step 2: substitute expression into both of the other equations and solve for one variable.

so we isolated x for the first equation and we got: x=16+5y-z we plug in x=16+5y-z to the other 2 equations. The other two equations are : 2x+3y+4z=18 and x+y-z=-8 so we plug in x=16+5y-z in place of x in the equations above 2(16+5y-z)+3y+4z=18 The 2 next to the parenthesis is being multiplied by the numbers and variables inside the parenthesis. This is called the distribution property. 2* 16=32 2*5y= 10y 2*-z= -2z ( negative times a positive always equals a negative) 32+10y-2z+3y+4z=18 we need to combine liked terms :liked terms are for example : there is a blue ball with strips and a blue ball with strips and a solid red one and a solid red one.... to make this easier to read and say you will add the balls that match up together.... there are 2 striped blue balls and 2 solid red balls. same with numbers.... 10y and 3y are liked terms because y.... They look alike... when added 10y+3y=13y 4z-2z=2z so now the equation is easier to read. 32+13y+2z=18 now we need to move 32 to the other side like we are isolating a variable. 13y+2z=-24 as of right now this equation is done... but we will need it later now lets plug in x=16+5y-2z into the second equation (16+5y-z)+y-z=-8 since there is no number in-front of the parenthesis to distribute we can move on to combining liked terms. 5y+y=6y -z-z=-2z (this a bit tricky -z -z=? think about it how many z's are there? 2... correct..... and the z's are what? negative.. so -2... but we forgetting something... we need everyone to know there was 2 negative Z's so it will be -2z) 16+6y-2z=-8 now we need to isolate the two variable..... so we need to move 16 by subtracting since 16 is positive 16+6y-2z=-8 -16 = -16 6y-2z=-24 Now we will need this answer in next study card.

Example of step 1

step 1: isolate a variable..... we have 3 equations x-5y+z=16 / 2x+3y+4z=18/ x+y-z=-8 So for step one i will use equation one. x-5y+z=16 isolate a variable X will be the easiest to isolate to isolate x we need to get the other numbers and variables on the other side. x-5y+z=16 +5y = +5y x+z=16+5y -z= -z x=16+5y-z Step one complete

step 4: substitute the value of one variable to find the value of the other variable. we found what y equals. and step 5: repeat step 4 as needed

y=-2 substitute 6y-2z=-24 6(-2)-2z=-24 6*-2=-12 -12-2z=-24 12 = 12 -2z=-12 /2 /2 z=6 now we found z and y now we just need to find x so we go to the very first equation x=16+5y-z and plug in value for y and z into the equation to find x x=16+5(-2)-6 5*-2 =-10 x=16-10-6 x=0 VARIABLE ANSWERS : y=-2 z=6 x=0