Ask question

Ask question

All categories

2 years ago

13

If you were to move use the substitution method to solve the following system choose the new equation after the expression equiv

alent to ask from the second equation is subject to dig into the first equation.
2x-3y=-29
x+4y=13

A) 2(4y+13)-3y=-29
B) 2(-4y+13)-3y=-29
C) 2x-3(4y+13)=-29
D) 2x-3(-4y+13)=-29

1 answer:

yanalaym [24]2 years ago

8 0

Solve x+4y = 13 for x by subtracting 4y from both sides.

We end up with x = -4y+13.

Since x and -4y+13 are the same, we can replace every x in the first equation with -4y+13

2x-3y = -29

2( x ) - 3y = -29

2( -4y+13 ) - 3y = -29 ... x is replaced with -4y+13

The answer is choice B

You might be interested in

a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

Step-by-step explanation:

The equation of a line:

$y=mx+b$

We have

$m=\dfrac{2}{3}$

substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}$

Convert the equation:

$y=\dfrac{2}{3}x+b$ |<em>subtract $y$ from both sides</em>

$\dfrac{2}{3}x-y+b=0$ |<em>multiply both sides by 3</em>

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

$(0,\ 0)\to x_0=0,\ y_0=0$

substitute:

$d=4$

$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

$4=\dfrac{|3b|}{\sqrt{13}}\qquad|$ |<em>multiply both sides by $\sqrt{13}$ </em>

$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |<em>divide both sides by 3</em>

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

4 0

2 years ago

Use substitution to determine the solution of the system of equations. Write the solution as an ordered pair.

zubka84 [21]

The answer is (6,4) x=6 y=4

5 0

2 years ago

Mrs steven is delivering flowers to a local flower shop she delivers the same number of flowers with each delivery the flower sh

jenyasd209 [6]

The answer is1612 after 4 trips

3 0

2 years ago

Read 2 more answers

List the sides of each triangle from shortest to greatest

Lelechka [254]

In every triangle, the largest side, is opposite the largest angle.

Also, the smallest side, is opposite the smallest angle.

a. $70^o\ \textgreater \ 60^o\ \textgreater \ 50^o$ so $|RQ|\ \textgreater \ |PR|\ \textgreater \ |PQ|$ ,

because RQ is opposite angle P, the largest,
PR is opposite angle Q , the middle
and PQ is opposite angle R, the smallest.

Greatest side: RQ

b. The sum of the measures of the interior angles of any triangle is 180°,

so

$m(A)+m(B)+m(C)=180^o\\\\50^o+45^o+x=180^o\\\\x=180^o-50^o-45^o=85^o$

thus, m(C) is the largest angle. This means the largest side is the side AB.

Answers:

a) RQ
b)AB

8 0

2 years ago

Which of these options for saving money typically offers the lowest interest rate?

Gwar [14]

D. savings account.....

5 0

3 years ago

Read 2 more answers