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Determine whether the lines will be perpendicular when graphed.
Y = mx +c
3x - 2y = 6
-2y=-3x+6
Gradient = 1.5
2x + 3y = 6
Gradient = - 0.6667
-0.6667 * 1.5 = - 1.000 therefore the lines will be perpendicular since the product of their gradients is -1.
Smoking section = x,
Non – smoking = 73 + 2x
Total number of seats = 73 + 2x + x = 205
3x = 205 – 73
3x = 132
X=
Smoking section = 44 seats.
Non – smoking = 73 +44 × 2 = 161= 161 seats
Solve the system of equations by the substitution method
x + 3y = 32 ………….. (i)
-3x + 2y = 3…………. (ii)
x = 32 – 3y …………… (iii)
Substituting equation (iii) into equation (ii) we get
- 3(32-3y) + 2y = 3
-96 + 9y + 2y = 3
-96+11y=3
11y = 99
y = 9
Equation (iii) x = 32 – 3y
x = 32 - 3×9
x = 5
Solve the system of equations
x + y = 5 ……… (i)
x - y = -9 ………(ii)
x = 5 – y …….. (iii)
(5 - y) – y = - 9
5 – 2y = - 9
-2y = -14
Y = 7
X = -2
A system of an equation refers to a collection of two or more linear equations which have the same set of variables. While solving a system of equations, we find the value of the unknown variables. The question below has two variables.
White = x
Red = 3x
x + 3x = 264.
4x = 264
X = 66
White should be 66 gallons while red should be 198 gallons.