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Hi I'm having trouble on solving systems and graphing them

User Charles G
by
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1 Answer

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The system of equations is

0 = 2y + 6 - x (1)

0 = 4y + 3x - 8 (2)

To solve it graphically we must find 2 points on each line

So let us choose values of x and find their corresponding values of y

Let x = 2

Substitute it in equation (1)

0 = 2y + 6 - (2)

Add the like terms on the right side

0 = 2y + (6 - 2)

0 = 2y + 4

Subtract 4 from both sides

0 - 4 = 2y + 4 - 4

-4 = 2y

Divide both sides by 2

-2 = y

The 1st point is (2, -2)

Let x = 4

Substitute it in the equation to find y

0 = 2y + 6 - (4)

0 = 2y + (6 - 4)

0 = 2y + 2

Subtract both sides by 2

0 - 2 = 2y + 2 - 2

-2 = 2y

Divide both sides by 2 to find y

-1 = y

The 2nd point is (4, -1)

Now you can plot these to points and join them to draw the 1st line

We will do the same with equation (2)

Let x = 4

Substitute it in the equation (2)

0 = 4y + 3(4) - 8

0 = 4y + 12 - 8

Add the like terms in the right side

0 = 4y + (12 - 8)

0 = 4y + 4

Subtract 4 from both sides

0 - 4 = 4y + 4 - 4

-4 = 4y

Divide both sides by 4

-1 = y

The 1st point on the second line is (4, -1)

Let x = -4

0 = 4y + 3(-4) - 8

0 = 4y -12 - 8

0 = 4y + (-12 - 8)

0 = 4y - 20

Add 20 to both sides

0 + 20 = 4y - 20 + 20

20 = 4y

Divide both sides by 4

5 = y

The 2nd point on the second line is (-4, 5)

Plot the two points and join them to form the second line

As you see the two lines have point (4, -1),

then the two lines will intersect at this point

The solution of the system is (4, -1)

User Pelle Jacobs
by
7.8k points

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