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GED Math : Linear Algebra

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Example Questions

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Example Question #11 : Standard Form

Rewrite the equation in standard form. $-3x =\frac{1}{4}y-2x$

Possible Answers:

20x+y=4

$-5x-\frac{1}{4}y = 1$

$\textup{The answer is not given.}$

4x+y=0

$-5x+\frac{1}{4}y = 1$

Correct answer:

4x+y=0

Explanation:

The equation in standard form is: Ax+By=C

Add on both sides.

$-3x+3x =\frac{1}{4}y-2x+3x$

Simplify both sides.

$0=\frac{1}{4}y+x$

If we multiply by four on both sides, we can eliminate the fraction.

$0\cdot 4=4(\frac{1}{4}y+x)$

0 = y+4x

The answer is: 4x+y=0

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Example Question #14 : Standard Form

What is the equation $y=\frac {1}{3}x+\frac {4}{5}$ in standard form?

Possible Answers:

-5x+15y=12

-5x+15y=-12

$-\frac {1}{3}x+y=\frac {4}{5}$

5x-15y=12

Correct answer:

-5x+15y=12

Explanation:

Step 1: Find the lowest common denominator of the fractions on the right. To find the lowest common denominator in this question, we multiply the denominators together because both denominators are both prime numbers. **In the cases where the denominators are either both composite or one prime/one composite, find the lowest common denominator by breaking down the factors of the two numbers and taking the product of the factors that are in common (sometimes you will need to add an uncommon factor).

So, lowest common denominator is $3\times5=15$ .

Step 2: Multiply both sides by 15.

$(15)y=(15)\times\frac {1}{3}x+(15)\times\frac {4}{5}$

Step 3: Simplify:

15y=5x+12

Step 4: Standard form is given when x and y are on the same side of the equation, usually written as Ax+By=C .

So, we need to move the over, and then we have our answer:

15y-5x=(5x-5x)+12

$\Rightarrow -5x+15y=12$

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Example Question #61 : Linear Algebra

Line

Give the equation, in standard form, of the line on the above set of coordinate axes.

Possible Answers:

3x+ 5y = 15

5x-3y = 15

3x-5y = 15

5x+3y = 15

Correct answer:

5x+3y = 15

Explanation:

The -intercept of the line can be seen to be at the point five units above the origin, which is (0, 5) . The -intercept is at the point three units to the right of the origin, which is (3,0) . From these intercepts, we can find slope by setting b= 5,a = 3 in the formula

$m = - \frac{b}{a}$

The slope is

$m = - \frac{5}{3}$

Now, we can find the slope-intercept form of the line

y = mx + b

By setting $m = - \frac{5}{3}$ , b= 5 :

$y = - \frac{5}{3}x +5$

The standard form of a linear equation in two variables is

ax+by = c ,

so in order to find the equation in this form, first, add $- \frac{5}{3}x$ to both sides:

$y + \frac{5}{3}x = - \frac{5}{3}x +5 + \frac{5}{3}x$

$\frac{5}{3}x+ y = 5$

We can eliminate the fraction by multiplying both sides by 3:

$3 \left (\frac{5}{3}x+ y \right )= 3 \cdot 5$

Distribute by multiplying:

$3 \cdot \frac{5}{3}x+3 \cdot y =15$

5x+3y = 15 ,

the correct equation.

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Example Question #12 : Standard Form

Write the given equation in standard form: 3+y =2(2x-6)

Possible Answers:

4x+y=-9

4x-2y =9

4x+y = 15

-4x+y = 9

-4x+y = -15

Correct answer:

-4x+y = -15

Explanation:

The equation in standard form is: Ax+By =C

Simplify the right side by distribution.

3+y =2(2x)-(2)(6)

y+3 = 4x-12

Subtract on both sides.

y+3 -4x= 4x-12-4x

The equation becomes:

-4x+y+3 = -12

Subtract 3 from both sides.

-4x+y+3-3 = -12-3

The answer is: -4x+y = -15

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Example Question #233 : Algebra

Given the point (1,3) with a slope of two, write the equation in standard form.

Possible Answers:

-2x-2y = 1

y=2x-1

2x-3y =-1

-2x+y = 1

2x+3y =-1

Correct answer:

-2x+y = 1

Explanation:

We will first need to write the point-slope form to set up the equation.

y-y_1 = m(x-x_1)

Substitute the slope and point.

y-3= 2(x-1)

Simplify the right side.

y-3 = 2x-2

Add 3 on both sides.

y-3+3 = 2x-2+3

y=2x+1

Subtract on both sides.

y-2x=2x+1-2x

The answer is: -2x+y = 1

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Example Question #11 : Standard Form

Find the equation in standard form: y=4(x-4)

Possible Answers:

-4x+y = -16

-4x+y = -4

-2x+y = -8

2x+y = -16

2x+y = -4

Correct answer:

-4x+y = -16

Explanation:

Distribute the right side.

y=4x-16

Subtract on both sides.

y-4x=4x-16-4x

The answer is: -4x+y = -16

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Example Question #235 : Algebra

Rewrite the equation in standard form: $\frac{1}{2}x = 2x-2y+3$

Possible Answers:

$\textup{The answer is not given.}$

4x+4y =-6

$y=\frac{3}{4}x +\frac{3}{2}$

4x-4y =-6

$\frac{3}{4}x +\frac{3}{2}y =1$

Correct answer:

4x-4y =-6

Explanation:

The standard form of a linear equation is: Ax+By=C

Multiply by two on both sides to eliminate the fraction.

$(\frac{1}{2}x)(2) =2( 2x-2y+3)$

x= 4x-4y+6

Subtract on both sides.

x-x= 4x-4y+6-x

0 = 4x-4y +6

Subtract 6 from both sides.

The answer is: 4x-4y =-6

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Example Question #61 : Linear Algebra

Given the slope is 3, and the y-intercept is 6, write the equation of the line in standard form.

Possible Answers:

x-3y=6

-3x+y= 6

3x-y= 6

x+3y=6

3x+y= 6

Correct answer:

-3x+y= 6

Explanation:

The standard form of a line is: Ax+By =C

First, we can write the equation in slope-intercept form: y=mx+b

y=3x+6

Subtract on both sides.

y-3x=3x+6-3x

The answer is: -3x+y= 6

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Example Question #21 : Standard Form

Given the slope of a line is 7, and a known point is (2,5), what is the equation of the line in standard form?

Possible Answers:

-7x+y =-9

-7x+y =-19

-7x+2y =-5

7x-3y =-5

-7x+y =-6

Correct answer:

-7x+y =-9

Explanation:

The standard form of a line is: Ax+By =C

We can use the point-slope form of a line since we are only given the slope and a point.

y-y_1 = m( x-x_1)

Substitute the slope and the point.

y-5 = 7( x-2)

Simplify this equation.

y-5 = 7x-14

Add on both sides.

y-5+5= 7x-14+5

y=7x-9

Subtract from both sides.

y- 7x=7x-9- 7x

Simplify both sides.

-7x+y =-9

The answer is: -7x+y =-9

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Example Question #238 : Algebra

Rewrite the equation in standard form: y= 4(x-2)

Possible Answers:

-x+4y = -8

-8x+4y = -1

-4x+y =2

-4x+y = -2

-4x+y = -8

Correct answer:

-4x+y = -8

Explanation:

Distribute the four through both terms of the binomial.

y=4x-8

Subtract on both sides of the equation.

y-4x=4x-8-4x

Simplify both sides.

-4x+y = -8

The answer is: -4x+y = -8

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GED Math : Linear Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Standard Form

Example Question #14 : Standard Form

Example Question #61 : Linear Algebra

Example Question #12 : Standard Form

Example Question #233 : Algebra

Example Question #11 : Standard Form

Example Question #235 : Algebra

Example Question #61 : Linear Algebra

Example Question #21 : Standard Form

Example Question #238 : Algebra

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