Which point satisfies the system of equations y = 3x − 2 and y = -2x + 3?

Mathematics

2 answers:

Sedbober [7]3 years ago

3 0

Answer:

(1,1)

Step-by-step explanation:

The choices are not visible, however are unnecessary to solve this problem.

Given y = 3x - 2 and y = -2x + 3

[Set them equal to each other]

3x - 2 = -2x + 3

[Find x]

3x + 2x - 2 = 3

3x + 2x = 5

5x = 5

x = 1

[Plug x = 1 to both equations to check and find y]

y = 3x - 2

y = 3(1) - 2 = 3 - 2 = 1

y = -2x + 3

y = -2(1) + 3 = -2 + 3 = 1

Both are equal to y = 1 when x = 1

The point is then: (1,1)

vfiekz [6]3 years ago

3 0

Answer:

(1, 1).

Step-by-step explanation:

y = 3x − 2

y = -2x + 3

Subtracting:

0 = 5x - 5

5x = 5

x = 1.

Put x = 1 into the first equation:

y = 3(1) - 2 = 1.

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nirvana33 [79]

Answer:

y+3=2(x-1)

Step-by-step explanation:

Point-slope form is $y-y_1 = m (x-x_1)$ . In order to write a linear equation using this form, the $y_1$ , $x_1$ and $m$ must be substituted by real numbers.

The $m$ represents the slope of the equation. We know that the answer has to be parallel to the line y=2x-1. y=2x-1 is already in slope-intercept form, or $y=mx+b$ , in which $m$ represents the slope. We can see that the $2$ is in place of that $m$ , therefore 2 is the slope of y=2x-1. Lines that are parallel have the same slope, so we know that the slope of the new equation must be 2 as well.

The $x_1$ and $y_1$ represent the x and y values of one point that the line passes through. We know that the new equation must pass through the point (1, -3), so we'll substitute 1 in place of the $x_1$ and -3 in place of the $y_1$ .

Substituting for those three values will give you an equation like this, therefore it is the answer:

$y-(-3)= 2(x-(1))$