System of Equations 2

Solving

Using Substitution

where the lines intersect.  So the solution could bewhich of the following?
A solution to a system of equations is
A single point (one ordered pair)
No solution (parallel lines; they don't intersect)
Infinite # of Solutions (same line)
all of the above
1. Solve for the other variable.
2. Substitute the # or expression in forthe isolated variable.
4. Isolate one of the variables.
3. Take the answer you got, and plug it into one of the equations to find the othervariable.
5. Write the ordered pair.
Put the steps in order for solving a system 
using the method of substitution.
4, 2, 1, 3, 5
1, 4, 2, 3, 5
2, 1, 4, 3, 5
4, 3, 2, 1, 5
{
Solve by Substitution.    Fill in the blanks. 
3x - 1 = 
2x - 1 = 5
y = 3x - 1
y = x + 5
2x = 6
x = 3
Answer (
y = 3 •
y = 
y = 8
9 - 1
,
- 1
)
Solve by substitution.  Fill in the blanks.
2           + 3y = 21   
{
y = 
(
2x + 3y = 21
x = 9
)
So, the solution is 
(
,
)
Solve by substitution.  Fill in the blanks.
{
y = -2x + 1
y = 4x - 5
= 4x - 5
(
,
)
Step 1:  Solve for x in the 2nd equation.
Step 2:  Substitute the expression into the otherequation.
Solve by Substitution.  Fill in the blanks.
Step 3:  Solve for y!
x = -2y - 1
{
y = 
3x - 2y = 13
x + 2y = -1
3
(
)
- 2y = 13
Step 5:  Write the ordered
             pair.
Step 4:  Substitute the 
y value into either equation.
The solution is:
(
,
)
Solve the system.
{
y = 4x + 2
y = 10
Answer:
(
,
)
Is (-4, -1) a solution of
{
3x - 2y = -10
5x - 11y = -9
?
yes
no
Solve the system.
{

2x - y = 1

y = 10
Answer:
(
,
)
Solve the system.
{

4x -2y = 10

x = 4

Answer:
(
,
)
Solve the system.
{

y = -5x + 1

5x + 2y = 7

Answer:
(
,
)

What would be the first step when solving

this system using substitution?

Substitute (7x - 5y) for x in the first equation

Substitute (x + 3) for y in the second equation

Substitute (y + 3) for y in the second equation

Substitute (y + 3) for x in the second equation

{

x = y + 3

7x - 5y = 19

There is no next step. 

    You are done.

Plug -3 in for x into

    either original equation

    to find y

What would the next step to find the solution?
{

-2x - y = -2

y = x - 1

Plug 1 in for y into either

    equation to find x

Plug 1 in for x into either

   original equation to find y 

-2x - (x - 1) = -2
-3x + 1 = -2
-3x = -3
x = 1

(This means they

are parallel lines!)

When our variables disappear and we are left

with a false statement, the answer is "no solution".

(This means they

are completely overlapping!)

When our variables disappear and we are left

with a true statement, the answer is "infinitely many".

Infinitely many

4x - 2y = 4

y = 2x - 2

4x - 2(2x - 2) = 4

4x - 4x + 4 = 4
4 = 4
Solve the system.
{

4x -2y = 10

y =2x +5

Infinitely many

No solution

Solve the system.
{

3x+ y = 6

y =

-3x + 6

Infinitely many

No solution

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