The <em><u>correct answers</u></em> are:
#1) no solution; #2) (3, 11), because both lines pass through this point
; #3) There is no graph to use to answer the question; #4) There is no graph to use to answer the question; #5) Line y = -2x + 3 intersects the line y = -x + 1; #6) There is no graph to use to answer the question; #7) There is no graph to use to answer the question; #8) 4h + 1 = 3h + 5
; #9) No solution; #10) (-6, -4)
Explanation:
#1) For the equations x+y=5 and x+y=4, if we were to eliminate a variable, we would wind up eliminating both variables and have unequal constants. Thus there is no solution.
#2) To solve the system y=x+8 and y=3x+2, we can substitute for y in the first equation:
3x+2 = x+8
Subtract x from each side:
3x+2-x = x+8-x
2x+2 = 8
Subtract 2 from each side:
2x+2-2 = 8-2
2x = 6
Divide both sides by 2:
2x/2 = 6/2
x = 3
Substitute this into the first equation:
y=x+8
y=3+8
y=11
This means that both lines pass through (3, 11) and this is the solution to the system.
#3) No graph to use to answer the question.
#4) No graph to use to answer the question.
#5) The slopes of the lines y = -2x+3 and y = -x+1 are different (-2 and -1). This means that the lines will intersect.
#6) No graph to use to answer the question.
#7) No graph to use to answer the question.
#8) To solve this, substitute the value of g in the first equation into g in the second equation:
4h+1 = 3h+5
#9) The slopes of these equations are the same, and the y-intercepts are different; this means that the lines are parallel and never intersect, so there is no solution.
#10) To solve this system, substitute the value of a from the second equation into the first equation:
a - 4b = 10
a = b-2
b - 2 - 4b = 10
Combine like terms:
-3b - 2 = 10
Add 2 to each side:
-3b - 2 + 2 = 10 + 2
-3b = 12
Divide both sides by -3:
-3b/-3 = 12/-3
b = -4
Substitute this value into the second equation:
a = b - 2
a = -4 - 2
a = -6
This gives us the solution (-6, -4)
