| << Chapter < Page | Chapter >> Page > |
Solve the system by substitution.
We need to solve one equation for one variable. Then we will substitute that expression into the other equation.
| Solve for
y .
Substitute into the other equation. |
 |
| Replace the y with −3 x + 5. |
 |
| Solve the resulting equation for x . |
 |
 | |
| Substitute x = 3 into 3 x + y = 5 to find y . |
 |
 | |
| The ordered pair is (3, −4). |
 |
| Check the ordered pair in both equations:
|
|
| The solution is (3, −4). |
In [link] it was easiest to solve for y in the first equation because it had a coefficient of 1. In [link] it will be easier to solve for x .
Solve the system by substitution.
We will solve the first equation for and then substitute the expression into the second equation.
 | |
| Solve for
x .
Substitute into the other equation. |
 |
| Replace the x with 2 y − 2. |
 |
| Solve the resulting equation for y . |
 |
|
Substitute y = 5 into x − 2 y = −2 to find x . |
 |
| The ordered pair is (8, 5). | |
| Check the ordered pair in both equations:
|
|
| The solution is (8, 5). |
When both equations are already solved for the same variable, it is easy to substitute!
Solve the system by substitution.
Since both equations are solved for y , we can substitute one into the other.
| Substitute for y in the first equation. |
 |
| Replace the y with |
 |
| Solve the resulting equation. Start
by clearing the fraction. |
 |
| Solve for x . |
 |
 | |
| Substitute x = 2 into y = to find y . |
 |
| The ordered pair is (2,1). | |
| Check the ordered pair in both equations:
|
|
| The solution is (2,1). |
Be very careful with the signs in the next example.
Solve the system by substitution.
We need to solve one equation for one variable. We will solve the first equation for y .
 | |
| Solve the first equation for y . |
 |
| Substitute −2 x + 2 for y in the second equation. |
 |
| Replace the y with −2 x + 2. |
 |
| Solve the equation for x . |
 |
 | |
|
Substitute into 4 x + 2 y = 4 to find y . |
 |
| The ordered pair is | |
| Check the ordered pair in both equations.
|
|
| The solution is |
In [link] , it will take a little more work to solve one equation for x or y .
Solve the system by substitution.
We need to solve one equation for one variable. We will solve the first equation for x .
 | |
| Solve the first equation for x . |
 |
| Substitute for x in the second equation. |
 |
| Replace the x with |
 |
| Solve for y . |
 |
 | |
 |
Since 0 = 0 is a true statement, the system is consistent. The equations are dependent. The graphs of these two equations would give the same line. The system has infinitely many solutions.
Notification Switch
Would you like to follow the 'Elementary algebra' conversation and receive update notifications?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|