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If x=a,y=b is the solution of the equations x+y=5 and 2x-3y =4, then the value of a and b are respectively

Sagot :

semsee45

Answer:

a = 3.8

b = 1.2

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x+y=5 \\2x-3y =4\end{cases}[/tex]

To solve the given system of equations, begin by rearranging the first equation to isolate y:

[tex]x+y=5\\\\y=5-x[/tex]

Now, substitute y = 5 - x into the second equation and solve for x:

[tex]2x-3(5-x)=4\\\\2x-15+3x=4 \\\\ 5x - 15 = 4 \\\\5x = 4 + 15 \\\\5x = 19 \\\\x=\dfrac{19}{5} \\\\ x = 3.8[/tex]

Finally, substitute x = 3.8 into y = 5 - x and solve for y:

[tex]y = 5 - 3.8 \\\\ y = 1.2[/tex]

Given that the solutions are x = a and y = b, then the values of a and b are:

[tex]\Large\boxed{\boxed{\begin{array}{l}a=3.8\\b=1.2\end{array}}}[/tex]

[tex]\dotfill[/tex]

Additional Notes

If you need the values of a and b as improper fractions, then:

[tex]a=\dfrac{19}{5}\\\\\\b=\dfrac{6}{5}[/tex]

Answer:

a = 3.8 , b = 1.2

Step-by-step explanation:

given the system of equations

x + y = 5 → (1)

2x - 3y = 4 → (2)

multiplying (1) by 3 and adding the result to (2) will eliminate y

3x + 3y = 15 → (3)

add (2) and (3) term by term to eliminate y

(2x + 3x ) + (- 3y + 3y ) = 4 + 15

5x + 0 = 19

5x = 19 ( divide both sides by 5 )

x = 3.8

substitute x = 3.8 into either of the 2 original equations and solve for y

substituting into (1)

3.8 + y = 5 ( subtract 3.8 from both sides )

y = 1.2

given x = a and y = b , then a = 3.8 and b = 1.2

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