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3 years ago

Solve the system of equations. y= 3x +5 y= 8x +3

Mathematics

2 answers:

Lady bird [3.3K]3 years ago

5 0

Answer:

y=6.2 and x=0.4 or (0.4,6.2)

Step-by-step explanation:

Since both expressions are equal to y, we can set them equal to each other and solve for x:

3x+5=8x+3

5=5x+3

2=5x

2/5=x

0.4=x

Now to solve y:

y=8(2/5)+3

y=16/5+3

y=3.2+3

y=6.2

Check answers:

6.2=3(0.4)+5

6.2=1.2+5

6.2=6.2

6.2=8(0.4)+3

6.2=3.2+3

6.2=6.2

Answers work, so y=6.2 and x=0.4 or (0.4,6.2) as an ordered pair

Ede4ka [16]3 years ago

5 0

Answer: x= 2/5 , y= 31/5

Step-by-step explanation:Let's work to solve this system of equations:

y= 3x +5 : Equation 1

y= 8x +3 : Equation 2

The tricky thing is that there are two variables, x and y. If only we could get rid of one of the variables...

subsitute y= 8x +3 : [8x+3=3x+5]

isolate x for 8x+3=3x+5: x+2/5

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What is the equation of the line that passes through (1, 2) and (8,9) in slope-intercept form?

Neporo4naja [7]

Answer:

The equation of line that passes through (1, 2) and (8,9) in slope-intercept form is: $y = x+1$

Step-by-step explanation:

The slope-intercept form of line is given by the formula:

$y = mx+b$

Here m is the slope and b is the y intercept

Given

$(x_1,y_1) = (1,2)\\(x_2,y_2) = (8,9)$

First of all, the slope has to be found

$m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{9-2}{8-1}\\m = 1$

Putting m=1 in the equation

$y = x+b$

Putting the point (1,2) in the equation to find the value of b

$2 = 1+b\\b = 2-1\\b = 1$

The equation is:

$y = x+1$

Hence,

The equation of line that passes through (1, 2) and (8,9) in slope-intercept form is: $y = x+1$

7 0

2 years ago

Which linear inequality is represented by the graph? y < 3x + 2 y > 3x + 2 y < 1/3x + 2 y > 1/3x + 2

andrey2020 [161]

Answer:

$y>3x+2$ is represented in the graph.

Step-by-step explanation:

To find the linear inequality for the shown graph.

Steps:

Finding the equation of dotted line shown in the graph.

Equation of line is given by

$y=mx+b$

where $m$ is slope of line and $b$ is y-intercept.

Given points: $(0,2) \ and\ (-3,-7)$

Slope of the line $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-7-2}{-3-0}$

$m=\frac{-9}{-3}$

∴ $m=3$

From the given points we can see that point of y-intercept is given i.e. the point where the line intersects the y-axis $(0,2)$

∴ $b=2$

So equation of line:

$y=3x+2$

Since the shaded area in the graph is above the line and the line is dotted this means that $y$ is greater than the equation of line.

So, the inequality can be given as:

$y>3x+2$

4 0

2 years ago

What are the $x$ - and $y$ -intercepts of the equation $3x+4y=24$ ?

Angelina_Jolie [31]

The x and the y-intercepts of the function are 8 and 6, respectively

<h3>Intercepts</h3>

The intercepts of a function are the points where the graph of the function crosses the x-axis

<h3>The function</h3>

The function is given as:

$3x + 4y = 24$

Set y to 0, to calculate the x-intercept

$3x + 4(0) = 24$

$3x = 24$

Divide both sides by 3

$x = 8$

Set x to 0, to calculate the y-intercept

$3(0) + 4y = 24$

$4y = 24$

Divide both sides by 4

$y = 6$

Hence, the x and the y-intercepts of the function are 8 and 6, respectively