Question

53) Solve the equation using substitution and elimination method. x + y = 5 and 2x -3y=4​

Answer 1

Answer:

Step-by-step explanation:

x+y=5

2x-3y=4​

Step 1: Solve one of the equations for either x = or y = . We will solve the first equation for y.

x+y=5

y=5-x

Step 2: Substitute the solution from step 1 into the second equation.

2x-3y=4

2x-3(5-x)=4

Step 3: Solve this new equation.

2x-3(5-x)=4

2x-15+3x=4

5x-15=4

5x-15+15=4+15

5x=19

x=3.8

Answer 2

Answer

we have, two equations

• x + y = 5 ........(i)
• 2x - 3y = 4 ........(ii)

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★ first solve by using substitution method

from eq(i) we get,

x = 5 - y .........(iii)

now, substitute the value of x from (iii) in (ii)

$\bold{↦ \: 2(5 - y) - 3y = 4} \\ \\ \bold{↦ \: 10 - 2y - 3y = 4} \\ \\ \bold{↦ \: 10 - 5y = 4} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{↦ \: 5y = 10 - 4} \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ ↦ \: 5y = 6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{↦ \: \boxed{ \pink {\bold{ y = \frac{6}{5}} }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now, substitute the value of y in (iii)

$\bold{↦ \: x = 5 - \frac{6}{5} } \: \: \\ \\ \bold{↦ \:x = \frac{25 - 6}{5} } \\ \\ \bold{↦ \boxed{ \pink{\bold{\: x = \frac{19}{5} }}}} \: \: \: \:$

hence,

value of x is 19/5 and value of y is 6/5

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★ now, solve by using elimination method

we have,

• x + y = 5 ........(i)
• 2x - 3y = 4 .......(ii)

multiply eq.(i) by 2

➪ 2(x + y) = 5 × 2

➪ 2x + 2y = 10 ........(iii)

now, subtract eq.(ii) from .(iii)

$\bold{↦ \: 2x + 2y - (2x - 3y) = 10 - 4} \\ \\ \bold{↦ \: \cancel{2x} + 2y - \cancel{2x} + 3y = 6} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{↦ \:2y + 3y = 6 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{↦ \: 5y = 6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{↦ \boxed { \pink{\bold{\:y = \frac{6}{5} }}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now, putting value of y in eq.(i)

$\bold{↦ \:x + \frac{6}{5} = 5 } \: \: \\ \\ \bold{↦ \: x = 5 - \frac{6}{5} } \: \: \\ \\ \bold{↦ \: x = \frac{25 - 6}{5} } \\ \\ \bold{↦ \: \boxed{ \pink{\bold{ x = \frac{19}{5} }}}} \: \: \: \:$

hence, value of x is 19/5 and value of y is 6/5