Consider the system:
2 answers:
Answer:
Step-by-step explanation:
In this problem, we have the following linear equations:
y=3x+5
y=ax+b
We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.
1. What values for a and b make the system inconsistent?
A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:
a=3
for any value of b
2. What values for a and b make the system consistent and dependent?
A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:
a=3 and b=5
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Answer:
We can model the decimal number 1.7 by drawing two squares and divide each of the two squares into 10 equal parts.
Then we start shading the square such that the first square is fully shaded and in the second square we shade 7 out of the 10 parts such that 0.7 of the figure is shaded.
Hence, the total portion of the figures that are shaded are:
1+0.7=1.7
