You start with: (assuming x equals the cost to enter and y the cost of going on the rollercoasters.)
x+5y=35
x+11y=59. Multiply the top equation by -1, and subtract the equations, giving you -6y=-24, divide by -6 into both sides of the equation, to get y=4. Now replace y in one of the original equations (I recommend x+5y=35) and solve for x, giving you x=15
The cost for entering is 15 dollars, while each coaster is 4 dollars more. You could simplify this by changing y into x and making it slope-intercept form, to track your cost. y=4x+15, so it has a slope of 4, and a y-intercept of 15. This answer should give you a good grade on a test.
#2
2x - 4y = -2
2x + 3y = -16
------------------subtract
-7y = 14
y = 14/-7
y = -2
2x - 4y = -2
2x - 4(-2) = -2
2x + 8 = -2
2x = -2 -8
2x = -10
x = -10/2
x = -5
answer x = -2 and y = -5
check:
2(-5)- 4(-2) = -2
-10 +8 = -2
-2 = -2.....true
2x + 3y = -16
2(-5)+3(-2) = -16
-10 + (-6) = -16
-16 = -16...true
X + 7x = 56 + 8
Simplifying x + 7x = 56 + 8 Combine like terms: x + 7x = 8x 8x = 56 + 8 Combine like terms: 56 + 8 = 64 8x = 64 Solving 8x = 64 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Divide each side by '8'. x = 8 Simplifying x = 8
Since the difference*4=36, the difference = 9
since the number-6= the difference, the number-6=9
Thus the number is 15
