All categories

3 years ago

Solve the system by substitution. - 8x + y = -32 - 3x – 10 = y (,)

Mathematics

2 answers:

Ket [755]3 years ago

4 0

Answer:

x = 2

y = -16

Step-by-step explanation:

Substitute value of y, -3x - 10 in the equation-8x + y = -32

-8x + (-3x - 10) = -32

-8x - 3x - 10 = -32

-11x - 10 = -32

-11x = -32 + 10

-11x = -22

Divide both sides by coefficient of x which is -11

x = 2

Substitute value of x, 2, in the equation-3x - 10 = y

(-3)2 - 10 = y

-6 - 10 = y

y = -16

agasfer [191]3 years ago

3 0

Answer:

$x=2,\:y=-16$

Step-by-step explanation:

$\begin{bmatrix}-8x+y=-32\\ -3x-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-8x+y=-32:\quad x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}x=-\frac{-32-y}{8}\\\begin{bmatrix}-3\left(-\frac{-32-y}{8}\right)-10=y\end{bmatrix}\\\\Simplify\\\begin{bmatrix}\frac{3\left(-32-y\right)}{8}-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{3\left(-32-y\right)}{8}-10=y:\quad y=-16\\\\\mathrm{For\:}x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}y=-16\\x=-\frac{-32-\left(-16\right)}{8}\\$

$-\frac{-32-\left(-16\right)}{8}=2\\x=2\\x=2,\:y=-16$

You might be interested in

GIVING BRAINLIEST what is 97 - 56 + 12

quester [9]

Answer:

Step-by-step explanation:

When subtracting 97-56=41+12=53. The answer is 53. Consider using a calculator or mental math next time rather than asking it as a question.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

8 0

3 years ago

Read 2 more answers

What is the equation of the line described below written in slope-iWhat is the equation of the line described below written in s

horsena [70]

The equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1

<h3>Equation of a line</h3>

A line is the shortest distance between two points. The equation of a line in point-slope form and perpendicular to a line is given as;

y - y1 = -1/m(x-x1)

where

m is the slope

(x1, y1) is the intercept

Given the following

Point = (4, -1)

Line: 2x-y - 7 = 0

Determine the slope

-y = -2x + 7

y= 2x - 7

Slope = 2

Substitute

y+1 = -1/2(x -4)

Write in slope-intercept form

2(y + 1) = -(x - 4)

2y+2 = -x + 4

2y = -x + 2

y = -1/2 + 1

Hence the equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1

Learn more on equation of a line here: brainly.com/question/13763238

#SPJ1

4 0

2 years ago

Please answer asap!!!

torisob [31]

fjsefkn jWESHGFcsVBU LJFWGVfyitWHJEasdasdaFsedfsEfSEfsefsesefsfseereeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

5 0

2 years ago

Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the

maksim [4K]

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

$y=ax^2+bx+c$

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

$x_v=-\frac{b}{2a}$

In this problem, we have:

$y=-x^2-6x-13$

Then:

a = -1

b = -6

We write now:

$x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3$

Part 3:

For this part, we need to find the x-intercepts. This is, when y = 0:

$-x^2-6x-13=0$

To solve this, we can use the quadratic formula:

$x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}$

And solve:

$x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}$ $x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}$

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0: