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3 years ago

How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2.x+ 2 6x – 4y = –10

Mathematics

2 answers:

fgiga [73]3 years ago

7 0

Answer:

its c

Step-by-step explanation:

no solution

Ira Lisetskai [31]3 years ago

4 0

Answer:

The system has one solution

Step-by-step explanation:

we have the system of equations

$y=\frac{2}{3}x+2$ ----> equation A

$6x-4y=-10$ ----> equation B

Solve the system by substitution

substitute equation A in equation B

$6x-4(\frac{2}{3}x+2)=-10$

$6x-\frac{8}{3}x-8=-10$

Solve for x

Multiply by 3 both sides to remove the fraction

$18x-8x-24=-30$

Combine like terms

$10x=-30+24$

$10x=-6$

$x=-\frac{6}{10}$

Simplify

$x=-\frac{3}{5}$

Find the value of y

$y=\frac{2}{3}(-\frac{3}{5})+2$

$y=-\frac{6}{15}+2$

$y=\frac{24}{15}$

Simplify

$y=\frac{8}{5}$

The solution of the system is the point $(-\frac{3}{5},\frac{8}{5})$

therefore

The system has one solution

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Which of the following point-slope form equations could be produced with the points (-5, -2) and (1, 2)?

Harman [31]

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-5, -2) and (1, 2). Substitute:

$m=\dfrac{2-(-2)}{1-(-5)}=\dfrac{2+2}{1+5}=\dfrac{4}{6}=\dfrac{2}{3}\\\\y-(-2)=\dfrac{2}{3}(x-(-5))\\\\\y+2=\dfrac{2}{3}(x+5)\to c.$

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3 years ago

Write an equation in slope intercept form for the line that passes through (-20,-6) with slope m=1/4

brilliants [131]

We start with the equation y-y1 =m (x-x1) because we have m the slope = 1/4 and a point on the line with the coordinates (x1=-20, y1=-6) so,

y+6=1/4 ( x+20);
y=(1/4)x + 20/4 -6;

y= (1/4)x -1 and this is the equation in slope intercept form y=mx +b where the lope m= 1/4 and b= -1 the y-intercept

Answer y= (1/4)x -1

5 0

3 years ago

Solve for the equation, show all your work. This is an absolute value equation. You need to show both equations and the work for

VMariaS [17]

Answer:

$x=-1$ or $7$

Step-by-step explanation:

We use casework on when $3x-9=12$ and when $3x-9=-12$ .

For the first case, $3x-9=12$ , we add 9 to both sides to get

$3x=21$ .

Dividing both sides by 3 gives

$x=7.$

For the second case, $3x-9=-12$ , we add 9 to both sides to get

$3x=-3$ .

Dividing both sides by 3 gives

$x=-1$ .

Checking both cases, we plug in $x=7$ and $x=-1$ .

For the first case, we have $|3(7)-9|=|21-9|=|12|=12$ , which satisfies the equation.

For the second case, we have $|3(-1)-9|=|-3-9|=|-12|=12$ , which also satisfies the equation.

This gives us two solutions to the equation; $x=7$ and $x=-1$ .

4 0

2 years ago

The perimeter of the rectangle below is 90 units. find the length of side vy . write your answer without variables.

Salsk061 [2.6K]

The picture in the attached figure

we know that
perimeter of a rectangle=2*[base+height]
base=3y+1
height=2y+3
perimeter=90 units
so
90=2*[(3y+1)+(2y+3)]-----> 90=2*[5y+4]----> 10y+8=90----> y=8.2 units

base=3y+1-----> base=3*8.2+1-----> 25.6 units
height=2y+3----> height= 2*8.2+3---> 19.4 units

the answer is
the length of side vy is (2y+3)-----> 19.4 units

3 0

3 years ago

A digital camera costs $185 and the sales tax rate is 5.7%. What is the total cost of the camera after tax

Dovator [93]

♥ To solve find how much this will cost AFTER the price increases.
♥ Solve:
Multiply the original price as it is by: 1.057 (5.7 as a decimal would be 0.057, but as i said to keep the original price, the 1 will keep it there.)
 $185 * 1.057 = $195.545$
Final answer: $195.54

7 0

3 years ago