Question

5x − y = 5 and 3x + 2y = 29 find the value of x and y

Answer 1

Step-by-step explanation:

Given:-

5x-y=5---(1)

3x+2y=29----(2)

To find:-

value of x and y

Solution:-

by multiplying 3 with eq (1) and 5 with eq (2) we get

15x-3y=15--(3)

15x+10y=145---(4)

by subtracting eq (4) from eq (3) we get

-13y=-130

$\implies{y={\frac{-130}{-13}}}$

$\implies{y=10}$

by putting the value of y in eq (1) we get

$5x-10=15$

$\implies{5x=15+10}$

$\implies{5x=25}$

$\implies{x={\cancel{\frac{25}{5}}}}$

$\implies{x=5}$

Hence the solution is

${\boxed{x=5,y=10}}$

Extra information:-

used method:-

Elimination method

Answer 2

Given: $5 x-y=5,3 x+2 y=29$

We have to find the value of x and y,

STEPS USING SUBSTITUTION

$5 x-y=5,3 x+2 y=29$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$5 x-y=5,3 x+2 y=29$

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign.

$5 x-y=5$

Add y to both sides of the equation.

$\text { Add } y \text { to both sides of the equation. }\\5 x=y+5\\\text { Divide both sides by } 5 \text {. }\\\\x=\frac{1}{5}(y+5)\\\\\text { Multiply } \frac{1}{5} \text { times } y+5\\\\x=\frac{1}{5} y+1\\\\\text { Substitute } \frac{y}{5}+1 \text { for } x \text { in the other equation, } 3 x+2 y=29 \text {. }\\\\3\left(\frac{1}{5} y+1\right)+2 y=29\\\\\frac{3}{5} y+3+2 y=29\\\\\frac{13}{5} y+3=29\\\\\frac{13}{5} y=26\\\\y=10$

$\text { Substitute } 10 \text { for } y \text { in } x=\frac{1}{2} y+1$

Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{1}{5} \times 10+1\\x=2+1\\x=3\\\\x=3, y=10$

We get, $x=3, y=10$