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Solving A System Of Equations

Solving A System Of Equations. By: Stephanie Heaton. For this exercise we will use the following equations to solve for x and y. 2x+y= 6 x+y=3. 3 Ways to Solve. When given a system of equations, there are three ways to solve for x and y. Substitution Elimination Graphing.

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Solving A System Of Equations

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  1. Solving A System Of Equations By: Stephanie Heaton

  2. For this exercise we will use the following equations to solve for x and y. 2x+y= 6 x+y=3

  3. 3 Ways to Solve • When given a system of equations, there are three ways to solve for x and y. • Substitution • Elimination • Graphing

  4. Select one of the equations. 1. 2x+y=6 x+y=6 Solving by Substitution • Ex. We will choose the second equation 2. x+y=6 we will solve for x. 2. Determine which term, x or y, to get by itself. • Ex. We will choose x to get by itself.

  5. 3. Now we want to solve for the variable we chose by getting it by itself on one side of the equality. 3. x+y=3 Solving By Substitution -y -y x=3-y • Ex. Subtract both sides by y to find x.

  6. 4. Now plug our x value into all the x values of the other equation. 4. 2x+y=6 Solving By Substitution 2(3-y)+y=6 -ex. Plug 3-y into the x of the first equation. 5. 2(3-y)+y=6 6-2y+y=6 6-y=6 5. Take that and solve for y. -6 -6 -y=0 y=0

  7. 6. Now we need to plug y back in the equation and solve for x. 6. 2x + y = 6 Solving by Substitution 2x + (0) = 6 2x = 6 2x/2 = 6/2 x=3 -plug 0 in for y and then solve for x by dividing both sides by 2. 7. x=3 y=0 7. Finally we have solved for both x and y. Menu

  8. Line up the two equations so that each term x and y in the first equation is lined up with the x and y from the second equation. 1. 2x+y=6 x+y=3 Solving by Elimination • 2. 2x+y=6 • - x+y=3 • 1x+0y=3 2. Now subtract like terms. • -subtract the x, subtract the y, subtract the constant. • 3. As we see in the example, the y’s canceled out and we have only one term (x) left in the equation. • 3. 1x = 3 • x=3

  9. 4. Now plug the x value we got in step 3 back into an equation and solve for y. 4. x=3 2x+y=6 2(3)+y=6 6+y=6 -6 -6 y=0 Solving by Elimination 5. We have now found the value for x and y. 5. x=3 and y=0 Menu

  10. To solve a system of equations by graphing first graph the two equations on a graph. 2x+y=6 x+y=3 Solving by Graphing 2x + y =6 • 2. Find the point where the two lines intersect. • -for our example the intersection of the lines is at (3,0) x + y = 3 (3,0)

  11. 3. The solutions to this problem is the point of intersection (3,0). So we know that x=3 and y=0. Solving by Graphing 2x + y = 6 x + y = 3 (3, 0) Menu

  12. If you still have questions make sure to ask your teacher for further explanation. Happy Math!

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