Which equations can be used to find the area?
2 answers:
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Answer:
<h2>a) x + y = -2</h2><h2>b) x - y = -8</h2><h2>c) 3x - 5y = -30</h2><h2>d) 5x + 3y = -16</h2>Step-by-step explanation:
Equation of line with slope m and passing through (x₁,y₁) is given by
y - y₁ = m ( x -x₁)
(x₁,y₁) = (−5,3)
a) Parallel to x = −1
Slope , m = -1
y - y₁ = m ( x -x₁)
y - 3 = -1 ( x -(-5))
y -3 = -x - 5
x + y = -2
b) Perpendicular to x = −1.
Slope of line x Slope of perpendicular line = -1
Slope of line x -1 = -1
Slope , m = 1
y - y₁ = m ( x -x₁)
y - 3 = 1 ( x -(-5))
y -3 = x + 5
x - y = -8
c) Parallel to y = 3 / 5 x + 2
Slope , m = 3/5
3x - 5y = -30
d) Perpendicular to y = 3 / 5 x + 2
Slope of line x Slope of perpendicular line = -1
Slope of line x 3/5 = -1
Slope , m = -5/3
5x + 3y = -16
When the given equations represent the same line, the number of points of intersection are infinite, such that the number of solutions are also infinite.
- The value of <em>b</em> that forms a system with infinite number of solutions is; <u>b = -8</u>
Reasons:
The equation the teacher wrote on the board is; 3·y + 12 = 6·x
The additional equation is; 2·y = 4·x + b
Required:
The value of <em>b</em>, such that the two equation form a system with infinitely many solutions.
Solution:
Two equations will have infinite number of solutions when they are the same equation, therefore, we have;
For the equation the teacher wrote;
3·y + 12 = 6·x
3·y = 6·x - 12
y = (6·x - 12) ÷ 3 = 2·x - 4
y = 2·x - 4
For the additional equation, we have;
2·y = 4·x + b
y = (4·x + b) ÷ 2 = 2·x + b÷2
Which gives;
When the two equations have infinitely many solutions, they will be equal, which gives;
b = -4 × 2 = -8
b = -8
<em>Which gives;</em>
<em>2·y = </em><em>4·x - 8</em>
- The value of <em>b</em> for which the additional equation 2·y = 4·x + b form a system of linear equation with infinitely many solutions is <u>b = -8</u>.
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