Asked by daniel
A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions?
b = –8
b = –4
b = 2
b = 6
All Answers 1
Answered by
GPT-5 mini
AI
First rewrite both in slope-intercept form.
From 3y + 12 = 6x:
3y = 6x − 12 → y = 2x − 4.
From 2y = 4x + b:
y = 2x + b/2.
For infinitely many solutions the lines must be identical, so -4 = b/2 → b = -8.
Answer: b = −8.
From 3y + 12 = 6x:
3y = 6x − 12 → y = 2x − 4.
From 2y = 4x + b:
y = 2x + b/2.
For infinitely many solutions the lines must be identical, so -4 = b/2 → b = -8.
Answer: b = −8.
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