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Illusion [34]
3 years ago
15

Learning task 2

Mathematics
1 answer:
patriot [66]3 years ago
3 0

The given equations are

2x-3y=-1\cdots(i) \\\\y=x-1\cdots(ii)

(a) Solution by graphing both the equations:

Graph for both the equations (i) and (ii) are in the figure. The point of intersection of both the graph is the solution of the equations.

From the graph, the point of intersection is (4,3)).

Hence, the required solution is (4,3).

(b) Solution by elimination method:

Equations (ii) can be written as -x+y=-1, now multiply it by 2, we have

-2x+2y=-2\cdots(iii)

Add equations (i) and (iii), we have

2x-3y=-1

-2x+2y=-2

__________

\Rightarrow -3y+2y=-1-2\\\\ \Rightarrow -y=-3\\\\ \Rightarrow y=3.

Putting the value of y=3 in equation (i), we have

2x-3\times 3=-1 \\\\\Rightarrow 2x=-1+9=8 \\\\\Rightarrow x=8/2=4

Hence, the required solution is (4,4).

(c) Solution by substitution method:

Substituting the value of y from equation (ii) to equation (i), we have

2x-3(x-1)=-1 \\\\\Rightarrow 2x-3x+3=-1 \\\\\Rightarrow -x=-1-4=-4 \\\\\Rightarrow x=4

Putting the value of x=4 in equation (i), we have

y=4-1=3.

Hence, the required solution is (4,3).

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