Question

Check whether the following equations are consistent or inconsistent. Solve them graphical
3/2x+5/3y=7.
9x-10y=12​

Answer 1

Step by step Explanation

Given:

$\frac{3}{2} x + \frac{5}{3} y = 7 \\ \\ 9x - 10y = 12$

To find: Check whether the following equations are consistent or inconsistent. Solve them graphical.

Solution:

Concept/Formula to be used:

Condition for consistency:

1) Unique Solution: $\bf \frac{a_1}{a_2} \neq\frac{b_1}{b_2}$

2) Infinitely many solutions:$\bf \frac{a_1}{a_2}=\frac{b_1}{b_2} =\frac{c_1}{c_2}$

If $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ are the equations.

Step 1: Write coefficients of x and y for both equations,and check for consistency

$a_1 = \frac{3}{2}$

$b_1 = \frac{5}{3}$

$a_2 = 9$

$b_2 = - 10$

$\frac{ \frac{3}{2} }{9} \neq\frac{ \frac{5}{3} }{ - 10}$

$\frac{3}{18} \neq\frac{ - 5}{30}$

$\frac{1}{6} \neq\frac{ - 1}{6}$

Thus, equations are consistent; having unique solution.

Step 2: Plot graph of both lines.

Find x and y intercept of both lines by putting y and x zero respectively.

Thus,

E(1.33,0) and C(0,-1.2) are the x and y intercept for line 9x-10y=12

B(4.67,0) and D(0,4.2) are the x and y intercept for line $\frac{3}{2} x + \frac{5}{3} y = 7$

Plot the points and draw both lines.

Both lines are intersected at A(3,1.5).

Therefore, this is the solution of equations.

Final answer:

Equations are consistent; having unique solution (3,1.5)

Hope it will help you.

Learn more:

1) Solve the following pair of linear equations graphically. Also write the observations.

(i) x + y = 1 ; 2x - 3y = 7

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2) solve the following system of linear equation graphically: 3x+y-11=0 and x-y-1=0

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