College Algebra : Linear Systems with Two Variables
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Example Questions
Example Question #11 : Linear Systems With Two Variables
Solve this linear system:
No solution
To solve this linear system we must find the coordinate point where both lines intersect. To do so, we eliminate one variable (by multiplying or dividing by some amount) and solve for the remaining variable.
1)
2)
Multiply equation 1 by 5 and equation 2 by 6; add the two equations to cancel out the x term:
1)
2)
Solve for y:
Now substitute this value back into either original equation to get the y-coordinate:
Rounded answer:
Example Question #12 : Linear Systems With Two Variables
Solve the system of equation using elimination:
To solve by elimination, we want to cancel out either the 
Now that we know the value of 
We can then conclude that
Example Question #13 : Systems Of Equations
Solve the following system of equations:
Solve by adding the two equations:
Adding the two equations yields the following:
Dividing both sides of the equation by 3 yields the following:
Plug value of x back into first equation:
Subtracting 3 from both sides of the equation yields the following:
Make sure the values for x and y satisfy both equations:
Solution: 
Example Question #13 : Linear Systems With Two Variables
Solve for 
We can evaluate the value of 
The equation becomes:
Substitute this value back into either the first or second equation, and solve for y.
The answer is:
Example Question #14 : Linear Systems With Two Variables
Consider the system of linear equations
True or false: This system has one and only one solution.
False
True
True
The given system has more equations than variables, which makes it possible to have exactly one solution.
One way to identify the solution set is to use Gauss-Jordan elimination on the augmented coefficient matrix
Perform operations on the rows, with the object of rendering this matrix in reduced row-echelon form.
First, a 1 is wanted in Row 1, Column 1. This is already the case, so 0's are wanted elsewhere in Column 1. Do this using the row operations:
An all zero row has been created, so it must be moved to the bottom:
Now, get a 1 into Row 2, Column 2:
Now, get 0's in the other positions in Column 2:
This matrix is in reduced row-echelon form, and can be interpreted to mean that
Thus, the system of equations given has one and only one solution.
Example Question #15 : Linear Systems With Two Variables
Solve this system of equations:
None of these
To solve this system of equations we must first eliminate one variable and solve for the remaining variable. We then substitute the variable back into our original equation and solve for the second variable still unknown.
We will use the elimination method:
Multiply the top equation by 1 and add it to the second equation:
--------------------------
Now we substitute the value of x into our original equation:
Thus, our lines are equal (intersect) at 
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