Solved on Sep 18, 2023

Find the value of $x$ where the equations $y=\frac{2}{3}x-4$ and $y=-4x+10$ intersect.

STEP 1

Assumptions1. The two equations given are $y=\frac{}{3} x-4$ and $y=-4 x+10$ . . We are looking for the value of $x$ where these two equations are equal.

STEP 2

Since both equations are equal to $y$ , we can set them equal to each other to find the value of $x$ .
$\frac{2}{} x -4 = -4x +10$

STEP 3

To solve for $x$ , we first need to get rid of the fractions. Multiply every term by3 to eliminate the fraction.
$3 \cdot \frac{2}{3} x -3 \cdot =3 \cdot -x +3 \cdot10$

STEP 4

implify the equation.
$2x -12 = -12x +30$

STEP 5

Next, we want to isolate $x$ on one side of the equation. Add $12x$ to both sides of the equation.
$2x +12x = -12x +12x +30$

STEP 6

implify the equation.
$14x =30$

STEP 7

Finally, divide both sides of the equation by14 to solve for $x$ .
$x = \frac{30}{14}$

STEP 8

implify the fraction to find the value of $x$ .
$x = \frac{15}{7}$ For the value of $x = \frac{15}{7}$ , the two equations $y=\frac{2}{3} x-4$ and $y=-4 x+10$ are equal.

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Find the value of $x$ where the equations $y=\frac{2}{3}x-4$ and $y=-4x+10$ intersect.

STEP 1

Assumptions1. The two equations given are $y=\frac{}{3} x-4$ and $y=-4 x+10$ . . We are looking for the value of $x$ where these two equations are equal.

STEP 2

Since both equations are equal to $y$ , we can set them equal to each other to find the value of $x$ .
$\frac{2}{} x -4 = -4x +10$

STEP 3

To solve for $x$ , we first need to get rid of the fractions. Multiply every term by3 to eliminate the fraction.
$3 \cdot \frac{2}{3} x -3 \cdot =3 \cdot -x +3 \cdot10$

STEP 4

implify the equation.
$2x -12 = -12x +30$

STEP 5

Next, we want to isolate $x$ on one side of the equation. Add $12x$ to both sides of the equation.
$2x +12x = -12x +12x +30$

STEP 6

implify the equation.
$14x =30$

STEP 7

Finally, divide both sides of the equation by14 to solve for $x$ .
$x = \frac{30}{14}$

STEP 8

implify the fraction to find the value of $x$ .
$x = \frac{15}{7}$ For the value of $x = \frac{15}{7}$ , the two equations $y=\frac{2}{3} x-4$ and $y=-4 x+10$ are equal.

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Find the value of xxx where the equations y=23x−4y=\frac{2}{3}x-4y=32​x−4 and y=−4x+10y=-4x+10y=−4x+10 intersect.

STEP 1

Assumptions1. The two equations given are y=3x−4y=\frac{}{3} x-4y=3​x−4 and y=−4x+10y=-4 x+10y=−4x+10. . We are looking for the value of xxx where these two equations are equal.

STEP 2

Since both equations are equal to yyy, we can set them equal to each other to find the value of xxx.2x−4=−4x+10\frac{2}{} x -4 = -4x +102​x−4=−4x+10

STEP 3

To solve for xxx, we first need to get rid of the fractions. Multiply every term by3 to eliminate the fraction.3⋅23x−3⋅=3⋅−x+3⋅103 \cdot \frac{2}{3} x -3 \cdot =3 \cdot -x +3 \cdot103⋅32​x−3⋅=3⋅−x+3⋅10

STEP 4

implify the equation.2x−12=−12x+302x -12 = -12x +302x−12=−12x+30

STEP 5

Next, we want to isolate xxx on one side of the equation. Add 12x12x12x to both sides of the equation.2x+12x=−12x+12x+302x +12x = -12x +12x +302x+12x=−12x+12x+30

STEP 6

implify the equation.14x=3014x =3014x=30

STEP 7

Finally, divide both sides of the equation by14 to solve for xxx.x=3014x = \frac{30}{14}x=1430​

STEP 8

implify the fraction to find the value of xxx.x=157x = \frac{15}{7}x=715​For the value of x=157x = \frac{15}{7}x=715​, the two equations y=23x−4y=\frac{2}{3} x-4y=32​x−4 and y=−4x+10y=-4 x+10y=−4x+10 are equal.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ where the equations $y=\frac{2}{3}x-4$ and $y=-4x+10$ intersect.

Assumptions1. The two equations given are $y=\frac{}{3} x-4$ and $y=-4 x+10$ . . We are looking for the value of $x$ where these two equations are equal.

Since both equations are equal to $y$ , we can set them equal to each other to find the value of $x$ .
$\frac{2}{} x -4 = -4x +10$

To solve for $x$ , we first need to get rid of the fractions. Multiply every term by3 to eliminate the fraction.
$3 \cdot \frac{2}{3} x -3 \cdot =3 \cdot -x +3 \cdot10$

implify the equation.
$2x -12 = -12x +30$

Next, we want to isolate $x$ on one side of the equation. Add $12x$ to both sides of the equation.
$2x +12x = -12x +12x +30$

implify the equation.
$14x =30$

Finally, divide both sides of the equation by14 to solve for $x$ .
$x = \frac{30}{14}$

implify the fraction to find the value of $x$ .
$x = \frac{15}{7}$ For the value of $x = \frac{15}{7}$ , the two equations $y=\frac{2}{3} x-4$ and $y=-4 x+10$ are equal.