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Solve each system by graphing. Check your solution.
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To Graph and Check: The system of equations by graphing method and check.
Answer to Problem 9P
Solution is (-5,0);
Explanation of Solution
Given information: The given equations are
And
Graph:
Use slope and y intercept method to graph the lines.
For equation (1)
Slope
Represent the y intercept (0,-2). Using slope find the another point.
Slope
Rise =-2
Run =5
So, from y intercept move down 2 units(because rise is -2) and right 5 units(because run is 5) to get another point. Then join the points and extend the line on both ends.
For equation (2)
Slope
Slope
Rise =-1
Run =1
So, represent the y intercept (0,-5) on xy plane. Using slope find another point. From y intercept move down 1 unit(because rise is -1) and right 1 unit(because run is 1) to get another point. Then join the points and extend the line.
The graph of the lines are
Interpretation: The Purple line represents equation (1) and Green line represents equation (2). Solution set is where the lines intersect. The solution set is (-5,0).
Check:
Plug in x as -5 and y as 0 into the equations then simplify to see whether the equations are true or not.
For equation (1)
Simplify the right side of the equation
Yes! The equation is true for the solution (-5,1) so, it is solution to the equation.
For equation (2)
Yes! The equation is true for (-5,0) so, this is solution to the equation.
Both equations are true for the solution set.
Hence the (-5,0) is the solution to the system of equations.
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High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
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