Question

Why is the system of equations 7x + 7y = 42 and 6x + y = 36 equivalent to the system of
equations x +y = 6 and 6x + y = 36? (1 point)
• The intercepts of the equations 7x + 7y = 42 and x + y = 6 are (0, 36) and (6, 0).
• The equation 7x + 7y = 42 can be multiplied by 7 to produce the equivalent equation x + y = 6.
• All equations share the point (6, 0).
• The intercepts of the equations 7x + Ty = 42 andx + y = 6 are (0, 6) and (6, 0).

Answer 1

Because 7x + 7y = 42 is the same equation as x + y = 6 (divide both sides by 7). So replacing 7x+7y=42 with x+y=6 gives an equivalent system — both equations represent the same line.