MATHEMATICS MIDDLE SCHOOL

What are the solutions to the system of equations?

Answers

Answer 1

Answer:

Answer:

A. $(1,5)$ and $(5,13)$

Step-by-step explanation:

We have been given a system of equations. We are asked to find the solution of our given system.

$\left \{ {{y=x^2-4x+8}\atop {y=2x+3}} \right.$

Equate both equations:

$x^2-4x+8=2x+3$

$x^2-4x-2x+8-3=2x-2x+3-3$

$x^2-6x+5=0$

Split the middle term:

$x^2-5x-x+5=0$

$x(x-5)-1(x-5)=0$

$(x-5)(x-1)=0$

Use zero product property:

$(x-5)=0\text{ (or) }(x-1)=0$

$x=5\text{ (or) }x=1$

Now, we will substitute both values of x, in our given equation to solve for y.

$y=2x+3$

$y=2(1)+3$

$y=2+3$

$y=5$

One solution: $(1,5)$

$y=2x+3$

$y=2(5)+3$

$y=10+3$

$y=13$

2nd solution: $(5,13)$

Therefore, option A is the correct choice.

Answer 2

Answer:

Answer:

Step-by-step explanation:

Given the 2 equations

y = x² - 4x + 8 → (1)

y = 2x + 3 → (2)

Since both express y in terms of x we can equate the left sides, that is

x² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 6x + 5 = 0 ← in standard form

(x - 1)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 5 = 0 ⇒ x = 5

Substitute these values into (2) for corresponding values of y

x = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)

x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)

Solutions are (1, 5) and (5, 13)

Related Questions

Help pleaseee?I've been stuck on this for a while.
The area of a rectangle is 82.84 square meters. If the length is 7.6 meters, then what is the width?hey i need help, anyone i don't get it do i divide or multiply HELPPPPP
Adam drew two same size rectangles and divided them into the same number of equal parts. He shaded one third of one rectangle and one fourth of other rectangle. what is the least number of parts into which both rectangles could be divided?
What's 20% as a decimal?
Vicki measured the midnight temperatures in 4 locations in Alaska. The temperatures were -7, -2, 1, 4. What is the mean absolute deviation of the temperatures?The mean is -1

Explain how the areas of a triangle and a parallelogram with the same height and base are related.

Answers

The triangle's area would be half of the parallelograms's area, since the formulas state that half of bh should be taken for the triangle's area.

A parallelogram with a base four times the height and an area less than 200 square feet

Answers

The area of a parallelogram is base multiplied by the height.
A parallelogram with a base four times the height and an area less than 200 square feet
B = 4H
Area < 200 square feet.

200 > B*H
200 > 4H * H
200 > 4H^2
50 > H^2
H ~ 5 square root of 2

Answer:196 square ft

Step-by-step explanation:.......................

7823 multiply10 to the power of 3.

Answers

The answer is 7,823,000

Answer: 7,823,000

Because 10 to the power of 3 means 1000, so 7823 times 1,000

What is 118/13=59/x

Answers

X=13/2 is that answer or do you need it in a different way

Justin works as a car salesman. Last week he had a total of 42,000 dollars in sales. if his Commission is 2 percent how much did Justin earn and last week?

Answers

2 percent of 42,000 dollars = $840 (ans)

Answer:

2% of $42,000 = $840

Step-by-step explanation:

The graph of a proportional relationship contains the point (20, 4).What is the corresponding equation?
Enter your answer as a fraction in simplest form in the box.

y = x