Question

2x-5y=9 3x+4y=2 solve the simultaneous equations

Answer 1

Answer:

x = 2

y= -1

Step-by-step explanation:

to solve this simultaneous equation, using substitution method, we say

let

2x-5y=9 ....................... equation 1

3x+4y=2....................... equation 2

from equation 2

3x+4y=2....................... equation 2

3x = 2-4y

divide both sides by 3

3x/3 = ( 2-4y)/3

x = ( 2-4y)/3 ......................... equation 3

substitute for x , x = ( 2-4y)/3in equation 3 in equation 1

2x-5y=9 ....................... equation 1

2(2-4y)/3 - 5y = 9

4 -8y/3 - 5y = 9

multiply through by 3

3 [(4-8y)/3] - 3(5y) = 3(9)

4 - 8y - 15y = 27

-23y = 27-4

-23y =23

divide both sides by the coefficient of y which is -23

-23y/-23 = 23/-23

y = -1

put y = -1 in equation 3

x = ( 2-4y)/3 ......................... equation 3

x = (2 -4(-1)]/3

x = (2 +4)/3

x = 6/3

x = 2

therefore the value of x and y is 2 and -1 respectively

Answer 2

$\huge\boxed{x=2;\ y=-1}$

$\left\{{{2x-5y=9}\atop{3x+4y=2}}\right$

First, we will solve the second equation for $x$. Subtract $4y$ from both sides of the second equation.

$3x=2-4y$

Divide both sides of the second equation by $3$.

$x=\frac{2}{3}-\frac{4}{3}y$

$\left\{{{2x-5y=9}\atop{x=\frac{2}{3}-\frac{4}{3}y}}\right$

Substitute the value of $x$ from the second equation into the first.

$\left\{{{2(\frac{2}{3}-\frac{4}{3}y)-5y=9}\atop{x=\frac{2}{3}-\frac{4}{3}y}}\right$

$2(\frac{2}{3}-\frac{4}{3}y)-5y=9$

We will solve the first equation for $y$.

Distribute the $2$ to the $(\frac{2}{3}-\frac{4}{3}y)$.

$\frac{4}{3}-\frac{8}{3}y-5y=9$

Combine the like terms.

$\frac{4}{3}-\frac{23}{3}y=9$

Add $\frac{4}{3}$ on both sides.

$-\frac{23}{3}y=9-\frac{4}{3}$

$-\frac{23}{3}y=\frac{23}{3}$

Divide both sides by $\frac{23}{3}$.

$-y=1$

Multiply both sides by $-1$.

$y=\boxed{-1}$

Substitute the value of $y$ into the second equation.

$\left\{{{y=-1}\atop{x=\frac{2}{3}-\frac{4}{3}y}}\right$

$x=\frac{2}{3}-\frac{4}{3}*-1$

Multiply.

$x=\frac{2}{3}+\frac{4}{3}$

Add.

$x=\frac{6}{3}$

$x=\boxed{2}$