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

Solving by Substitution

1. Select one of the equations.

1. 2x+y=6

x+y=6

2. Determine which term, x or y, to get by itself.

2. x+y=6

we will solve for x.

• Ex. We will choose the second equation

• Ex. We will choose x to get by itself.

Solving By Substitution

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

– Ex. Subtract both sides by y to find x.

-y -y

x=3-y

Solving By Substitution

4. Now plug our x value into all the x values of the other equation.

4. 2x+y=6

-ex. Plug 3-y into the x of the first equation.

5. Take that and solve for y.

2(3-y)+y=6

5. 2(3-y)+y=66-2y+y=66-y=6-6 -6-y=0

y=0

Solving by Substitution

6. Now we need to plug y back in the equation and solve for x.

6. 2x + y = 6

Menu7. Finally we have solved for both x and y.

7. x=3

y=0

-plug 0 in for y and then solve for x by dividing both sides by 2.

2x + (0) = 6

2x = 6

2x/2 = 6/2

x=3

Solving by Elimination1. 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

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.

2. 2x+y=6- x+y=3

1x+0y=3

3. 1x = 3

x=3

Solving by Elimination

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=0Menu5. We have now found

the value for x and y.5. x=3 and y=0

Solving by Graphing

1. To solve a system of equations by graphing first graph the two equations on a graph.

2x+y=6

x+y=3

x + y = 3

2x + y =6

(3,0)2. Find the point where the

two lines intersect.-for our example the

intersection of the lines is at (3,0)

Solving by Graphing

3. The solutions to this problem is the point of intersection (3,0). So we know that x=3 and y=0.

x + y = 3

2x + y = 6

(3, 0)

Menu

If you still have questions make sure to

ask your teacher for further explanation.

Happy Math!