Is (6,3) a solution to this system of equations y=3x - 3 3x - y =3

The point that is not the solution to the system of inequalities is (2, 3), the correct option is A.

What is a System of Inequality?

A system of Inequality is a set of inequalities in one or more variables.

The inequalities in the graph have a common solution shown by the shaded area.

The points (1,3), (0,3) and (0,4) lie in the shaded region.

Point (2,3) is out of the shaded area.

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For a point to be a solution, it has to be on the green shaded area including the solid red line to the left above the intersection of the lines but not the dashed red line to the right.

(2, 3) is outside the shaded area, so it is not a solution.

(1, 3) is inside the green shaded area, so it is a solution.

(0, 3) is on the red line above the intersection, so it is a solution.

(0, 4) is inside the green shaded area, so it is a solution.

Answer: A. (2, 3)

Answer:

To find the x-intercepts of the parabola defined by the equation y = 2x² - 8x + 10, you need to set y equal to zero (because x-intercepts occur when y is zero) and solve for x.

So, you have:

0 = 2x² - 8x + 10

Now, you can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 2, b = -8, and c = 10. Plug these values into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Since the discriminant (the value inside the square root) is negative, there are no real solutions, which means this parabola does not have x-intercepts in the real number system.

So, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts because there are no x-intercepts for this parabola in the real number system.

Step-by-step explanation:

Certainly, let's find the x-intercepts step by step for the equation:

y = 2x² - 8x + 10

Step 1: Set y to zero because x-intercepts occur when y equals zero:

0 = 2x² - 8x + 10

Step 2: Now, we want to solve this equation for x. We can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this formula:

a is the coefficient of the x² term (which is 2 in this case).

b is the coefficient of the x term (which is -8).

c is the constant term (which is 10).

Step 3: Plug the values of a, b, and c into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

Step 4: Simplify the equation inside the square root:

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Step 5: Now, notice that we have a square root of a negative number (√(-16)). In the real number system, we can't take the square root of a negative number. This means there are no real solutions for x.

Step 6: Since there are no real solutions, there are no x-intercepts for this parabola in the real number system. Therefore, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts in this case.

Answer:

The two numbers are: 42 and 7

Step-by-step explanation:

let x be the one number and y be the other number..

As per the statement:

One number is six times another number. Their difference is 35.

⇒               .....[1]

and

              .....[2]

Substitute equation [1] into [2] we get;

Combine like terms;

Divide both sides by 5 we get;

y = 7

Substitute the value of y =7 in [1] we get;

Therefore, the two numbers are: 42 and 7