Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If
the system has one solution, name it.
y = -x + 5
y = x - 3
a) one solution; (1, 4)
b) infinitely many
c) no solution
d) one solution; (4, 1)
y = -x + 5
y = x - 3
a) one solution; (1, 4)
b) infinitely many
c) no solution
d) one solution; (4, 1)
1 answer:
Answer:
d) one solution; (4, 1)
Step-by-step explanation:
It often works well to follow problem directions. A graph is attached, showing the one solution to be (4, 1).
_____
You know there will be one solution because the lines have different slopes. Each is in the form ...
y = mx + b
where m is the slope and b is the y-intercept.
The first line has slope -1 and y-intercept +5; the second line has slope 1 and y-intercept -3. The slope is the number of units of "rise" for each unit of "run", so it can be convenient to graph these by starting at the y-intercept and plotting points with those rise and run from the point you know.
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Step-by-step explanation:
[tex] - 24 \div 4 = \\ \frac{ - 24}{4} \\ = \frac{ - 12}{2} \\ = /frac{-6}{1}