Answer:
Step-by-step explanation:
Given system of equations in the question are,
-3x + y = -6
y =
We can rewrite these equation as,
-3x + y = -6
y = 3x - 6 ------(1)
Table of input-output values for this equation will be,
x 0 1 2 3 4
y -6 -3 0 3 6
y = ------(2)
Table for this equation will be
x 0 2 4 6 8
y -1 0 1 2 3
By plotting these points on the graph we find (2, 0) is a common point in both the tables,
Therefore, (2, 0) is the only one solution of the given system of equations.
<h3>Geometric Sequence: a(r)ⁿ⁻¹</h3>
1) a₁ = 2, r = 3
a) First five terms: 2, 6, 18, 54, 162
b) nth term: 2(3)ⁿ⁻¹
c) The 10th term: 2(3)¹⁰⁻¹ = 39366
2) a₁ = 243, r = 1/3
a) First five terms: 243, 81, 27, 9, 3
b) nth term: 243(1/3)ⁿ⁻¹
c) The 10th term: 1/81
3) a₁ = 6, r = 2
a) First five terms: 6, 12, 24, 48, 96
b) nth term: 6(2)ⁿ⁻¹
c) The 10th term: 3072
4) a₁ = 5, r = -1/10
a) First five terms: 5, -1/2, 1/20, -1/200, 1/2000
b) nth term: 5(-1/10)ⁿ⁻¹
c) The 10th term: -5 × 10⁻⁹
Based on the calculations, the coordinates of the y-intercept are (0, -9).
<h3>What is the y-intercept?</h3>
In Mathematics, the y-intercept of any graph (parabola) occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
<h3>How to calculate the slope of a line?</h3>
Mathematically, the slope of any straight line can be calculated by using this formula;
Substituting the given parameters into the formula, we have;
Slope, m = (-4.5 - 3)/(-3 + 8)
Slope, m = -7.5/5
Slope, m = -1.5.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (-8, 3), we have:
y - 3 = -1.5(x + 8)
y - 3 = -1.5x - 12
y = -1.5x - 12 + 3
y = -1.5x - 9
Therefore, the coordinates of the y-intercept are (0, -9).
Read more on slope and y-intercept here: brainly.com/question/24787293
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Like in a graph? or just on a line?
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