Question

plz draw a graph with solution ​

Answer 1

We've been given two equations that we need to plot on a graph.

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In order to plot them, we'll need pairs of x and y coordinates for each line which when joined will result in a line for the given equation. We'll be using the hit and trial method to find the x and y co-ordinate for a given equation.

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[3 pairs will be sufficient for one equation]

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For the line 5x - 4y = 8:

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Case I: x = 0

➝ 5x - 4y = 8

➝ 5(0) - 4y = 8

➝ -4y = 8

➝ y = (8)/(-4)

➝ y = -2

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∴ Pair 1: (0, -2)

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Case II: x = 4

➝ 5x - 4y = 8

➝ 5(4) - 4y = 8

➝ 20 - 4y = 8

➝ -4y = 8 - 20

➝ -4y = -12

➝ y = (-12)/(-4)

➝ y = (12)/(4)

➝ y = 3

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∴ Pair 2: (4, 3)

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Case III: x = 8

➝ 5x - 4y = 8

➝ 5(8) - 4y = 8

➝ 40 - 4y = 8

➝ -4y = 8 - 40

➝ -4y = -32

➝ y = (-32)/(-4)

➝ y = (32)/(4)

➝ y = 8

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∴ Pair 3: (8, 8)

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Therefore, the coordinates for the line 5x - 4y = 8 will be;

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$\begin{array}{|c|c|c|c|}\sf x& \ \sf 0 \ & \ \sf 4 \ & \ \sf 8 \ \\ \ \sf y \ & \ \sf -2 \ & \ \sf 3 \ & \ \sf 8\\ \end{array}$

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Plot these points on the graph, and connect them forming a straight line.

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For the line 7x + 6y = 9:

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Case II: x = 9

➝ 7x + 6y = 9

➝ 7(9) + 6y = 9

➝ 63 + 6y = 9

➝ 6y = 9 - 63

➝ 6y = -54

➝ y = -54/6

➝ y = -9

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∴ Pair 1: (9, -9)

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Case II: x = 3

➝ 7x + 6y = 9

➝ 7(3) + 6y = 9

➝ 21 + 6y = 9

➝ 6y = 9 - 21

➝ 6y = -12

➝ y = -12/6

➝ y = -2

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∴ Pair 2: (3, -2)

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Case III: x = 0

➝ 7x + 6y = 9

➝ 7(0) + 6y = 9

➝ 6y = 9

➝ y = 9/6

➝ y = 3/2

➝ y = 1.5

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∴ Pair 3: (0, 1.5)

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Therefore, the coordinates for the line 7x + 6y = 9 will be;

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$\begin{array}{|c|c|c|c|}\sf x& \ \sf 9 \ & \ \sf 3 \ & \ \sf 0 \ \\ \ \sf y \ & \ \sf -9 \ & \ \sf -2 \ & \ \sf 1.5 \ \\ \end{array}$

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Plot these points on the graph, an‎d connect them forming a straight line.

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Graph details:

Black line: 5x - 4y = 8

Blue line: 7x + 6y = 9

Scale: 5 units on the x-axis & 5 units on the y-axis

Answer 2

Step-by-step explanation:

• 5x-4y=8------(1)
• 7x+6y=9----(2)

From eq(1)

5x-4y=8

==>5x=8+4y

==>x=8+4y/5

Table:-

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$\boxed{\begin{array}{|c|c|c|}\sf x& \ \sf 0 \ & \ \sf 4 \\ \ \sf y \ & \ \sf -2 \ & \ \sf 3 \\ \end{array}}$

From eq(2)

7x+6y=9

==>7x=9-6y

==>x=9-6y/7

Table:-

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$\boxed{\begin{array}{|c|c|c|}\sf x& \ \sf 9 \ & \ \sf 3 \\ \ \sf y \ & \ \sf -9 \ & \ \sf -2 \ \ \\ \end{array}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thinlines\put(0,0){\vector(1,0){10}}\put(0,0){\vector(-1,0){1}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(0,-1){9}}\thicklines\put(0,-2){\circle*{0.5}}\put(4,3){\circle*{0.5}}\put(9,-9){\circle*{0.5}}\put(3,-2){\circle*{0.5}}\put(0,-2){\vector(4,3){7}}\put(9,-9){\vector(3,-2){6}}\end{picture}$