How many solutions does the system have?
Compare the slopes and intercepts. Different slopes give one solution. Same slope and same intercept give infinitely many. Same slope and different intercepts give none.
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How many solutions does the system y = −x + 7 and y = −x + 7 have? Write one, none or infinite.
Answer: infinite
How many solutions does the system y = −4x + 5 and y = −4x + 4 have? Write one, none or infinite.
Answer: none
How many solutions does the system y = −x − 4 and y = −x − 4 have? Write one, none or infinite.
Answer: infinite
Tip: Compare the slopes and intercepts. Different slopes give one solution. Same slope and same intercept give infinitely many. Same slope and different intercepts give none.
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