What is the solution to the system of equations? {x+2y=10y=12x+3

Mathematics

1 answer:

Marianna [84]3 years ago

5 0

The solution to given system of equations are $(x,y) = (\frac{4}{25} , \frac{123}{25})$

Solution:

Given that we have to find solution to the system of equations

Given equations are:

x + 2y = 10 ------ eqn 1

y = 12x + 3 ------ eqn 2

We can solve the above equations by substitution method

Substitute eqn 2 in eqn 1

x + 2(12x + 3) = 10

x + 24x + 6 = 10

25x = 10 - 6

25x = 4

$x = \frac{4}{25}$

Substitute the above value of x in eqn 2

$y = 12(\frac{4}{25}) + 3\\\\y = \frac{48}{25} + 3\\\\y = \frac{48+75}{25}\\\\y = \frac{123}{25}$

Thus the solution to given system of equations are $(x,y) = (\frac{4}{25} , \frac{123}{25})$

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Answer:

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3 0

3 years ago

ASAP HELP FOR NUMBER 13!!

horrorfan [7]

Problem 13a

Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.

Another point on this line is (3,8) which is drawn from the second column.

Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2

Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2

Plug those into y = mx+b and we get y = 2x+2

Answer: y = 2x+2

==============================================
Problem 13b

(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20

Another point on this line is (3,8) as drawn from the second column

Slope:
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4

Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20

Answer: y = -4x+20

==============================================
Problem 13c

(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.

Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5

Note: the fraction 3/2 is equivalent to the decimal form 1.5

Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2

So we can now update y = mx+b to y = 1.5x+2

Answer: y = 1.5x+2

Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write $y = \frac{3}{2}x+2$
==============================================
Problem 13d

(0,20) is on the line. So the y intercept is 20, indicating that b = 20

(3,11) is also on the line

Again as done with 13a-13c, I'm only looking at the first two columns.

Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3

Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier

Answer: y = -3x+20

6 0

3 years ago

If f(x)=2(x)^2+5\sqrt((x+2)), complete the following statement f(0)=

DENIUS [597]

Answer: 5

Step-by-step explanation:

$f(x)=2(x)^2+5\\\\f(0)=2(0)^2+5\\\\.\qquad =0+5\\\\.\qquad =5$