ANSWERS
• PART A,: ,the graph of the first equation is wrong
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• PART B,: ,(6/5, 9/5)
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• PART C,: ,see explanation
EXPLANATION
PART A
The mistake Hunter did was graphing the first equation, in blue. The y-intercept is 3, that is correct, but the slope is -1, so the line is wrong,
This means that (2, 5) is not the solution of the system.
PART B
The solution of this system is found easier with another method. Using the substitution method, we can substitute the second equation in the first equation,
[tex]x+(4x-3)=3[/tex]
Add like terms,
[tex]5x-3=3[/tex]
Add 3 to both sides,
[tex]\begin{gathered} 5x-3+3=3+3 \\ 5x=6 \end{gathered}[/tex]
And divide both sides by 5,
[tex]x=\frac{6}{5}[/tex]
Now, replace x with 6/5 in the second equation to find y,
[tex]y=4\cdot\frac{6}{5}-3=\frac{24}{5}-3=\frac{9}{5}[/tex]
Hence, the solution is (6/5, 9/5).
PART C
The solution to a system of equations is the point where the two graphs of the functions intersect, so they have the same value.
To use a table, we would complete the same table for a series of values of x, then complete with the values of y for each function. The solution to the system will be when both functions have the same value for the same x-value.
