All categories

2 years ago

© y= 2x + 6 -3x - 5y= 22 Please help with substitution

Mathematics

2 answers:

umka21 [38]2 years ago

7 0

Answer:

[2] x = -5y - 4

// Plug this in for variable x in equation [1]

[1] 2•(-5y-4) - 5y = 22

[1] - 15y = 30

// Solve equation [1] for the variable y

[1] 15y = - 30

[1] y = - 2

// By now we know this much :

x = -5y-4

y = -2

// Use the y value to solve for x

x = -5(-2)-4 = 6

Solution :

{x,y} = {6,-2}

Processing ends successfully

Subscribe to our mailing list

Email Address

Terms and Topics

Linear Equations with Two Unknowns

Solving Linear Equations by Substitution

You might be interested in

What is the definition of similarity? *

a_sh-v [17]

Answer:

D) If there is a sequence of rigid transformations and dilations, that take one figure to the other, then they are similar.

4 0

2 years ago

Which shows an equation in point-slope form of the line shown?

kramer

Answer: Option (3)

Step-by-step explanation:

The slope of the given line is

$\frac{-2-4}{-6-2}=\frac{-6}{-8}=\frac{3}{4}$

Thus, the answer must be Option (3)

4 0

2 years ago

What does the value of the 3 in the number 2358916

geniusboy [140]

The answer is 300,000

8 0

3 years ago

Read 2 more answers

6n=0.12 what is the answer and i need it fast

uranmaximum [27]

6n=0.12
n=0.12:6
n=0.02
Answer: n=0.02

4 0

3 years ago

A line passes through the points (-7, 2) and (1, 6).A second line passes through the points (-3, -5) and (2, 5).Will these two l

BlackZzzverrR [31]

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

Explanation:

Step 1. The first line passes through the points:

(-7,2) and (1,6)

and the second line passes through the points:

(-3,-5) and (2,5)

Required: State if the lines intersect, and if so, find the solution.

Step 2. We need to find the slope of the lines.

Let m1 be the slope of the first line and m2 be the slope of the second line.

The formula to find a slope when given two points (x1,y1) and (x2,y2) is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using our two points for each line, their slopes are:

$\begin{gathered} m_1=\frac{6-2}{1-(-7)} \\ \\ m_2=\frac{5-(-5)}{2-(-3)} \end{gathered}$

The results are:

$\begin{gathered} m_1=\frac{6-2}{1-(-7)}=\frac{4}{1+7}=\frac{4}{8}=\frac{1}{2} \\ \\ \end{gathered}$ $m_2=\frac{5+5}{2+3}=\frac{10}{5}=2$

The slopes are not equal, this means that the lines are NOT parallel, and they will intersect at some point.

Step 3. To find the intersection point (the solution), we need to find the equation for the two lines.

Using the slope-point equation:

$y=m(x-x_1)+y_1$

Where m is the slope, and (x1,y1) is a point on the line.

For the first line m=1/2, and (x1,y1) is (-7,2). The equation is:

$y=\frac{1}{2}(x-(-7))+2$

Solving the operations:

$\begin{gathered} y=\frac{1}{2}(x+7)+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+7/2+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+5.5 \end{gathered}$

Step 4. We do the same for the second line. The slope is 2. and the point (x1,y1) is (-3, -5). The equation is:

$\begin{gathered} y=2(x-(-3))-5 \\ \downarrow\downarrow \\ y=2x+6-5 \\ \downarrow\downarrow \\ y=2x+1 \end{gathered}$

Step 5. The two equations are:

$\begin{gathered} y=\frac{1}{2}x+5.5 \\ y=2x+1 \end{gathered}$

Now we need to solve for x and y.

Step 6. Equal the two equations to each other:

$\frac{1}{2}x+5.5=2x+1$

And solve for x:

$\begin{gathered} \frac{1}{2}x+5.5=2x+1 \\ \downarrow\downarrow \\ 5.5-1=2x-\frac{1}{2}x \\ \downarrow\downarrow \\ 4.5=1.5x \\ \downarrow\downarrow \\ \frac{4.5}{1.5}=x \\ \downarrow\downarrow \\ \boxed{3=x} \end{gathered}$

Step 7. Use the second equation:

$y=2x+1$

and substitute the value of x to find the value of y:

$\begin{gathered} y=2(3)+1 \\ \downarrow\downarrow \\ y=6+1 \\ \downarrow\downarrow \\ \boxed{y=7} \end{gathered}$

The solution is x=3 and y=7, in the form (x,y) the solution is (3,7).

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

6 0

1 year ago