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Elimination Method

Solve for x...

Question

Solve for $x$ and $y$
$\frac{3}{2} x + \frac{5}{3} y = 7$ and $9 x - 10 y = 14$

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Solution

$6 \times \frac{3}{2} x + \frac{5}{3} y = 7 ⟹ 9 x + 10 y = 42$
Adding both the equations $18 x = 56 ⟹ x = \frac{28}{9}$
$y = \frac{7}{5}$

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Similar questions

Q. Evaluate for

x

y

\frac{3}{2} x + \frac{5}{3} y = 7

9 x - 10 y = 14

Q. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

\frac{c_{1}}{c_{2}}

, find out whether the following pair of linear equations are consistent, or inconsistent.
(i)

3 x + 2 y = 5; 2 x - 3 y = 7

2 x - 3 y = 8; 4 x - 6 y = 9

\frac{3}{2} x + \frac{5}{3} y = 7; 9 x - 10 y = 14

5 x - 3 y = 11; - 10 x + 6 y = - 22

\frac{4}{3} x + 2 y = 8; 2 x + 3 y = 12

Q. Solve the following equations.
(1) 17p − 2 = 49
(2) 2m + 7 = 9
(3) 3x + 12 = 2x − 4
(4) 5(x − 3) = 3(x + 2)

(5)

\frac{9 x}{8}

\frac{y}{7}

\frac{y - 4}{3}

= 2

(7) 13x − 5 =

\frac{3}{2}

(8) 3(y + 8) = 10(y − 4) + 8

(9)

\frac{x - 9}{x - 5}

\frac{5}{7}

\frac{y - 4}{3}

\frac{b + (b + 1) + (b + 2)}{4}

x

y

x + y = 7

2 x + 3 y = 18

.

Q. Solve the following linear equations for

x

y

3 x + 2 y = 5

2 x - 3 y = 7

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