How many solutions? Systems in standard form
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 x + y = −3 and x + y = −7 have? Write one, none or infinite.
Answer: none
How many solutions does the system 3x + y = −8 and −3x + y = 4 have? Write one, none or infinite.
Answer: one
How many solutions does the system −5x + y = −8 and −5x + y = −11 have? Write one, none or infinite.
Answer: none
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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