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In Exercises 1 -5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions. using set notation to express their solution sets.
{y=4y+13x−2y=13
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To calculate: The number of solutions of a system {y=4x+13x+2y=13
Answer to Problem 1RE
Solution:
The solution of the system of equation is unique with coordinates {(1,5)}.
Explanation of Solution
Given information:
The system of equations {y=4x+13x+2y=13
Calculation:
Let us consider the system of equations as given below:
y=4x+1 (I)
3x+2y=13 (II)
Put the value of y from equation (I) in to equation (II) and compute the value of x as given below:
3x+2(4x+1)=133x+8x+2=1311x=11x=1
Put the value of x in equation (I) and compute the value of y as given below:
y=5
And check the equation y=4x+1 for a test point x=−3,y=−11
−11=4(−3)+1−11=−11
Which is correct.
And check the equation 3x−2y=13 for a test point x=−3,y=−11
3(−3)−2(−11)=13−9+22=1313=13
Which is also correct.
Therefore, the solution of the equations is unique x=−3,y=−11
Thus, solution set of system of equation is {(1,5)} and the solution is unique.
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Chapter 7 Solutions
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