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2 years ago

What is the solution to this system of equations?

Mathematics

1 answer:

mixas84 [53]2 years ago

5 0

Answer:

(-2,4)

Step-by-step explanation:

The solution is the point at which the two lines intersect, (-2,4). That point is the only one that satisfies (works) in both equations:

y = x + 6

4 = -2 + 6

and

y = -0.5x + 3

4 = -0.5(-2) + 3

4 = 1 + 3

====

You can also solve it algebraically:

y = x + 6

y = -0.5x + 3

-0.5x + 3 = x + 6 [Use the value of y from the second equation in the first equation]

-1.5x = 3

x = -2

Use this is y = -2 + 6:

y = 4

(-2,4)

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Translate this sentence into an equation. The product of Craig's savings and 4 is 76 . Use the variable c to represent Craig's s

pantera1 [17]

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4 0

3 years ago

Part C

makkiz [27]

a = 1, b =14 and y-coordinate is 6 when x = 0.

Solution:

Let us first write the equation of a line.

Take the points are (2, 2) and (6, 10).

Slope of the line:

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

$$m=\frac{10-2}{6-2}$

$$m=\frac{8}{4}$

m = 2

Point-slope formula:

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

y - 10 = 2(x - 2)

y - 10 = 2x - 4

Add 10 on both sides,we get

y = 2x + 6

Equation of a line is y = 2x + 6.

To find (a, 8), substitute x = a and y = 8 in the equation,

8 = 2a + 6

Subtract 6 from both sides, we get

2 = 2a

a = 1

To find (4, b), substitute x = 4 and y = b in the equation,

b = 2(4) + 6

b = 8 + 6

b = 14

Substitute x = o in the equation.

y = 2(0) + 6

y = 6

The y-coordinate is 6 when x = 0.

7 0

2 years ago

2x+5y=-21 , -2x+3y+-27

Elis [28]

Answer:

x=4.5 and y= -6

Step-by-step explanation:

2x+5y= -21

-2x+3y= -27

add the two equations: 8y= -48

y=-48/8= -6

sub for y in 2x+5y= -21

2x + 5(-6)=-21, 2x-30= -21

2x= -21+30= 9

x= 9/2=4.5

8 0

2 years ago

neil has 3 partially full cans of white paint. They contain 1/3 gallon, 1/5 gallon, and 1/2 gallon of paint about how much paint

tensa zangetsu [6.8K]

Answer: 31/30 gallons, or 1 and 1/30 gallons

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2 years ago

Find the solution to the system of equations represented by this matrix equation using an inverse matrix.

8090 [49]

Answer:

D) $\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right]$

Step-by-step explanation:

For matrix $\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

the inverse matrix is the transpose of the cofactor matrix, divided by the determinant: $\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]$

Your inverse matrix is: $\dfrac{1}{2(-3)-(1)(2)}\left[\begin{array}{cc}-3&-1\\-2&2\end{array}\right]$

so the solution is ...

$\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{cc}\frac{3}{8}&\frac{1}{8}\\\frac{1}{4}&-\frac{1}{4}\end{array}\right] \cdot\left[\begin{array}{c}2\\4\end{array}\right] =\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right] \qquad\text{matches selection D}$

4 0

3 years ago