Question

Solve 3x+2y=4, 2x-3y=7 by substitution method

Answer 1

Step-by-step explanation:

Here is the complete explanation of the problem

Answer 2

Answer:

The solutions of the given simultaneous equations are

$\boxed{\red{\sf\:x\:=\:2}}$

$\boxed{\red{\sf\:y\:=\:-\:1}}$

Step-by-step-explanation:

The given simultaneous equations are $\sf\:3x\:+\:2y\:=\:4\:\:-\:-\:-(\:1\:)\\\\\sf\:2x\:-\:3y\:=\:7\:\:-\:-\:-(\:2\:)$

Now,

$\sf\:2x\:-\:3y\:=\:7\:\:\:-\:-\:-\:(\:2\:)\\\\\implies\sf\:2x\:=\:7\:+\:3y\\\\\implies\sf\:x\:=\:\dfrac{7\:+\:3y}{2}$

Now, by substituting the value of x in equation ( 1 ), we get,

$\sf\:3x\:+\:2y\:=\:4\:\:\:-\:-\:-\:(\:1\:)\\\\\implies\sf\:3\:\times\:(\:\dfrac{7\:+\:3y}{2}\:)\:+\:2y\:=\:4\\\\\implies\sf\:\dfrac{21\:+\:9y}{2}\:+\:2y\:=\:4\\\\\implies\sf\:\dfrac{21\:+\:9y\:+\:4y}{2}\:=\:4\\\\\implies\sf\:21\:+\:9y\:+\:4y\:=\:4\:\times\:2\\\\\implies\sf\:21\:+\:13y\:=\:8\\\\\implies\sf\:13y\:=\:8\:-\:21\\\\\implies\sf\:13y\:=\:-\:13\\\\\implies\sf\:y\:=\:-\:\frac{\cancel{13}}{\cancel{13}}\\\\\implies\boxed{\red{\sf\:y\:=\:-\:1}}$

Now, by substituting this value of y in

$\sf\:x\:=\:\dfrac{7\:+\:3y}{2}$, we get,

$\sf\:x\:=\:\dfrac{7\:+\:3y}{2}\\\\\implies\sf\:x\:=\:\dfrac{7\:+\:3\:\times\:(\:-\:1\:)}{2}\\\\\implies\sf\:x\:=\:\dfrac{7\:-\:3}{2}\\\\\implies\sf\:x\:=\:\frac{\cancel4}{\cancel2}\\\\\implies\boxed{\red{\sf\:x\:=\:2}}$