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3 years ago

Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.

2 answers:

7 0

Lets try substitution5x+2y=21=5x=21-2y=x=(21-2y)/5

sub into second equation

-2(21-2y)/5+6y=-34(-42+4y)/5+6y=-34solve for yy=-64/17plug into equation and solve for x=(97/17)

pentagon [3]3 years ago

3 0

Answer:

The y-coordinate of the solution would be $-\frac{64}{17}$

Step-by-step explanation:

Given system of equations,

5x+2y = 21 ----------(1)

-2x+6y = -34 ---------(2),

2 × Equation (1) + 5 × Equation (1),

We get,

4y + 30y = 42 - 170

34y = -128

$\implies y = -\frac{128}{34}=-\frac{64}{17}$

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John's method to determine the width of the stream uses the knowledge

that the tangent of 60° is approximately 1.7.

The proper sequence John would use to find the width of the stream are;

Step 1; John drives a stake opposite the tree to establish a line between two points

Step 2; John uses a compass to walk away from the stakes at a right angle

Step 3; On the path John walks until he finds a line of sight to the tree that equals 60 degrees

Step 4; John drives a second stake in the ground

Step 5; John measures the the distance between the two stakes

Step 6; John multiplies the distance between the two stakes by 1.7 to find the distance.

Reasons:

The steps that can be used to measure the width of the stream are;

Step 1: Drive a stake opposite the tree on the other side of the stream.

Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.

Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60°.

Step 4; At the point where the line of sight to the tree is 60°, a second stake is driven in the ground.

Step 5; Measure the distance between the stakes that are placed in the ground.

Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60°) ≈ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.

$\displaystyle tan(60^{\circ}) = \mathbf{\frac{Width \ of \ stream}{Distance \ between \ stakes}}$