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Chapter 3: Q20. (page 149)

Find the point at which the graphs of2x+3y=7and3x鈭�4y=2intersect.

Short Answer

Expert verified

The graph intersects at the point2,1.

Step by step solution

01

– Use elimination method

The given equations are,

2x+3y=73x鈭�4y=2

....(1)....(2)

Multiply (1) by 3 and multiply (2) by 2, we get

6x+9y=216x鈭�8y=4

It can be rewritten as follows,

6x+9y鈭�21=06x鈭�8y鈭�4=0

....(3)....(4)

Subtracting equation (4) from (3), we get

(6x+9y鈭�21)鈭�(6x鈭�8y鈭�4)=06x+9y鈭�(6x鈭�8y)=21鈭�46x+9y鈭�6x+8y=1717y=17y=1717y=1

02

– Substitute the value of y in equation (1)

We know that y=1.

Substituting the value, we get

2x+3y=72x+3(1)=72x+3=72x=7鈭�32x=4x=2

Thus, the point at which the graph intersects is(2,1).

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