Question

Solve using any appropriate method. If the system has an infinite number of solutions, use set-builder notation to write

Answer 1

Answer:

$13.\ (x,y) = (-4,3)$

$14.\ No\ Solution$

$15.\ (x,y) = (-12,-32)$

$16.\ (x,y) = (3.75,6.25)$

$17.\ No\ Solution$

Explanation:

13)

$4x + 8y = 8$ ---- (1)

$5x + 7y = 1$ ------ (2)

Multiply equation by 5 and equation 2 by 4

$5(4x + 8y = 8)$

$4(5x + 7y = 1)$

$5 * 4x + 5 * 8y = 5 * 8\\4*5x + 4*7y = 4 *1$

$20x + 40y = 40$ ------ (3)

$20x + 28y = 4$ ------ (4)

Subtract equation 3 from 4

$(20x + 28y = 4) - (20x + 40y = 40)$

$20x - 20x+ 28y -40y= 4-40$

$-12y = -36$

Divide both sides by -12

$\frac{-12y}{-12} = \frac{-36}{-12}$

$y = 3$

Substitute $y = 3$ in equation 1

$4x + 8y = 8$

$4x + 8(3) = 8$

$4x + 24 = 8$

Subtract 24 from both sides

$4x + 24 - 24 = 8 - 24$

$4x = -16$

Divide both sides by 4

$\frac{4x}{4} = \frac{-16}{4}$

$x = -4$

$Hence\ (x,y) = (-4,3)$

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14)

$7x + 7y = 8$ ---- (1)

$5x + 5y = 10$ ----- (2)

Make x the subject of formula in (2)

$5x + 5y = 10$

$5x + 5y - 5y = 10 - 5y$

$5x = 10 - 5y$

$\frac{5x}{5} = \frac{10 - 5y}{5}$

$x = \frac{10}{5} - \frac{5y}{5}$

$x = 2 - y$

Substitute $x = 2 - y$ in (1)

$7x + 7y = 8$

$7(2-y) + 7y = 8$

Open bracket

$7*2-7*y + 7y = 8$

$14 -7y + 7y = 8$

$14 \neq 8$

At this point, we conclude that thee system has no solution.

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15)

$y = 3x + 4$ --- 1

$5x + y = -92$ ----2

Substitute $y = 3x + 4$ in (2)

$5x + 3x + 4 = -92$

$8x + 4 = -92$

Subtract 4 from both sides

$8x + 4 -4= -92 -4$

$8x = -96$

Divide both sides by 8

$\frac{8x}{8} = \frac{-96}{8}$

$x = -12$

Substitute $x = -12$ in equation 1

$y = 3x + 4$

$y = 3(-12) + 4$

$y = -36 + 4$

$y = -32$

$Hence\ (x,y) = (-12,-32)$

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16)

$0.4x + 0.4y = 4$

$0.4x - 0.4y = 1$

Add both equations

$(0.4x + 0.4y = 4) + (0.4x - 0.4y = 1)$

$0.4x+0.4x + 0.4y-0.4y = 4+1$

$0.8x = 5$

Divide both sides by 0.8

$\frac{0.8x}{0.8} = \frac{5}{0.8}$

$x = 6.25$

Substitute $x = 6.25$ in (1)

$0.4(6.25) + 0.4y = 4$

$2.5 + 0.4y = 4$

Subtract 2.5 from both sides

$2.5 -2.5 + 0.4y = 4 -2.5$

$0.4y = 1.5$

Divide both sides by 0.4

$\frac{0.4y}{0.4} = \frac{1.5}{0.4}$

$y = \frac{1.5}{0.4}$

$y = 3.75$

$Hence,\ (x,y) = (3.75,6.25)$

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17)

$x - 4y = 1$

$x= 7+ 4y$

Substitute $x= 7+ 4y$ in (1)

$7 + 4y - 4y = 1$

$7 \neq 1$

At this point, we conclude that thee system has no solution.