Good morning everybody . we will take you on a fun learning today. Mrs. Panchaporn Kantayasakun. New generation S.W.K. Mrs. Khrongsri Nampoon. By :. Mrs. Jarin Promsri. System of Linear Equations.
Good morning everybody.we will take you on a fun learning today.
New generation S.W.K
System of Linear Equations
How to: solve by graphing, substitution, linear combinations, and special types of linear systems
Ways to Solve Linear Systems
1. Solve one equation for one of its variables
2. Substitute that expression into the other equation and solve for the other variable
3. Substitute that value into first equation; solve
4. Check the solution
Here’s the problem:Equation one-x+y=1Equation two2x+y=-2
First, solve equation one for y
y = x+1
Next, substitute the above expression in for “y” in equation two, and solve for x
Congratulations! You now know x has a value of –1…but you still need to find “y”.
To do so…
First, write down equation one
So, now what?
You’re done; simply write out the solution as (-1,0)
***Did you remember?
To write a solution, once you’ve found x and y, you must put x first and then y: (x,y)
Solving Linear Systems by Linear Combinations
2. After looking at the coefficients of x and y, you need to multiply one or both equations by a number that will give you new coefficients for x or y that are opposites.
3. Add the equations and solve for the unknown variable
4. Substitute the value gotten in step 3 into either of the original equations; solve for other variable
5. Check the solution in both original equations
Solve the linear system
Equation 1: 3x+5y=6
Equation 2: -4x+2y=5
3x+5y= 6 --------
-4x+2y= 5 --------
12x+20y= 24 --------
3 ;3(-4x+2y) = 35
-12x +6y= 15 --------
+ ; 12x+ 20y -12x + 6y = 24 + 15
26y = 39
Equation 2: -4x+2y=5
Substitute the value you just found for
-4x+2( ) = 5
-4x+3 = 5
-4x = 2
The solution to the example system is ( )
A Final way to Solve Systems:
Graph and Check
Step 1 Download Application Quick graph from programe App Store.
Answer to the equation is the graph intersect (-1,0)
Equation one: 3x-4y=10
Equation two: 5x+7y=3
Equation one: x-6y=-19
Equation two: 3x-2y=-9
Equation one: x+3y=7
Equation two: 4x-7y=-10
Equation one: x+2y=5
Equation two: 3x-2y=7
Equation one: 3x-5y=-4
Equation two: -9x+7y=8