Question

How do you solve the system using the elimination method for $2x + 3y = 7$ and ${\text{3x + 4y = 10}}$?

Answer 1

Hint: It is given that we have to solve the given system of simultaneous equations by elimination method so multiply the first equation by $3$ and multiply the second equation by $2$ then subtract these equations. After subtracting we will find that $y$ will be eliminated and then simplify and get the value of $x$.

Complete step-by-step solution:
The two equations given in the question as below
$2x + 3y = 7{\text{ }}........{\text{(1)}}$
$3x + 4y = 10..........(2)$
We need to multiply the first equation by $3$ and multiply the second equation by $2$ then add these equations.
$2x + 3y = 7{\text{ }}........{\text{(1)}}$ Multiply By $3$
$3x + 4y = 10..........(2)$ Multiply By $2$
We get, $6x + 9y = 21$
              $6x + 8y = 20$
After subtracting both the equation, we get
$\Rightarrow$$(6x - 6x) + (9y - 8y) = 21 - 20$
$\Rightarrow$$y = 1$
Substituting this value of $y$ in the equation $1$ we get,
$\Rightarrow$$2x + 3(1) = 7$
$\Rightarrow$$2x + 3 = 7$
We are taking the integer of the left-hand side to the right-hand side
$\Rightarrow$$2x = 7 - 3$
$\Rightarrow$$2x = 4$
To eliminate $x$ we get,
$\Rightarrow$$x = \dfrac{4}{2}$
On dividing we get,
$\Rightarrow$$x = 2$

From the above solving equations by the elimination method, we have found the value of $x = 2{\text{ and y = 1}}{\text{.}}$

Note: We can verify the answer which we got by substitute the getting points in any one of the given equation First we are done from the equation $1.$
So, we are putting the attained points $x = 2$ and $y = 1$ in the equation $(1)$
We know the equation $(1)$ is as below
$2x + 3y = 7$
On putting the points in the equation$(1)$, we get
$2(2) + 3(1) = 7$
We just multiply the brackets numbers to the attached numbers respectively and then added to the left-handed side and we get,
$4 + 3 = 7$
$7 = 7$
Hence, the left-hand side is equal to the right-hand side.
So, our solution for the question is correct.