1001 Algebra Problems.PDF

Set 20 (Page 51)

305. c.Adding the two equations together yields
     the equation 10a= –40, the solution of which
     is a= –4. Now, substitute –4 in for ain the first
     equation and solve for b:

5(–4) + 3b= –2

–20 + 3b= –2

3 b= 18

b= 6

306. d.Add the two equations together to get the
     equation –2y= 8, which simplifies to y= –4.
     Next, substitute –4 for yin the second equa-
     tion and solve for x:

x– 5(–4) = –3

x+ 20 = – 3

x= – 23

307. b.In the first equation, multiply the (x+ 4)
     term by 3 to obtain 3(x+ 4) = 3x+ 12. Then,
     subtract 12 from both sides of the equation, so
     that the first equation becomes 3x– 2y= –7.
     Now, add the two equations together to obtain

- x= 1, or x= –1.

   308. d.First, multiply the second equation by 2 to

      obtain y+8x= 24. Then, subtract the first

      equation from this one to obtain 6x= 18,

      which simplifies to x= 3.

   309. bFirst, simplify the second equation by sub-

      tracting 9 from both sides of the equation. The

      second equation becomes –2x– 6 = y. Then,

      multiply the equation by 2 and add it to the

      first equation to obtain –6 = –y, the solution of

      which is y= 6. Now, substitute the value ofy

      into the first equation and solve for x:

4 x+ 6 = –3(6)

4 x+ 6 = –18

4 x= –24

x= –6

Since x= –6 and y= 6, the value ofxy= – 66 = –1.

310. e.First, multiply the first equation by –4 to
     obtain 28a– b= –100. Then, add this to the
     second equation to obtain 29a= –87,a= –3.
     To find b, substitute this value into the second
     equation to obtain b+ (–3) = 13, so b= 16.


311. b.In the first equation, multiply the (m+ n)
     term by 2 and add mto obtain

2(m+ n) + m= 2m+ 2n+ m= 3m+ 2n

Now, subtract the second equation from the

first equation to obtain the equation 5n= –15,

which simplifies to n= –3.

312. a.Simplifying the left side of the first equation
     results in 14a+ 21b= 56. Multiplying the sec-
     ond equation by –7 yields –7b– 14a = 28.
     Now, adding these two equations together
     yields 14b= 84, the solution of which is b= 6.

x

y

–10 –8 –6 –4 –2 2 4 6 8 10

–2

–4

–6

–8

–10

10

8

6

4

2

ANSWERS & EXPLANATIONS–