PLEASE HELP!!!!!!!!The system of equations is inconsistent.
What are the missing values?

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Accepted Answer

[tex]5x+ay=2 \\
bx+3y=8[/tex]Write it in the y=mx+b form.[tex]ay=-5x+2 \\
3y=-bx+8 \\ \\
y=-\frac{5}{a}x+\frac{2}{a} \\
y=-\frac{b}{3}x+\frac{8}{3}[/tex]The system will be inconsistent when the equations describe two parallel lines.Two lines are parallel when their slopes are identical. [tex]-\frac{5}{a}=-\frac{b}{3} \\
ab=(-5) \times (-3) \\
ab=15[/tex]Also they can't be the same line, so the y-intercepts must be different.[tex]\frac{2}{a} \not= \frac{8}{3} \\
8a \not= 2 \times 3 \\
8a \not= 6 \\
a \not= \frac{6}{8} \\
a \not= \frac{3}{4}[/tex]So for every value of a and b such that ab=15 and a≠3/2 this system of equations is inconsisent.It can be:[tex]5x+5y=2 \\
3x+3y=8 [/tex]or[tex]5x+15y=2 \\
x+3y=8[/tex]or[tex]5x+\frac{1}{2}y=2 \\