Question

What is the solution of the system? Use the elimination method. {4x+2y=182x+3y=15 Enter your answer in the boxes.

Answer 1

Answer:

x=3

y=3

Step-by-step explanation:

Given : $4x+2y=18\\2x+3y=15$

To solve : Solution of system of equation

Solution :

$4x+2y=18$  ---(a)

$2x+3y=15$ ---(b)

Since we are given that we have to solve these equation by elimination method :

Multiply equation (a) by 2 and equation (b) by 4

Then equation becomes:

$8x+4y=36$  ---(a)

$8x+12y=60$ ---(b)

Subtract (a) from (b)

$8x+12y-60-(8x+4y-36)=0$

$8x+12y-60-8x-4y+36=0$

$8y-24=0$

$y=\frac{24}{8}$

$y=3$

Now put this value in (b) to get value of x

$8x+12(3)=60$

$8x+36=60$

$8x=60-36$

$8x=24$

$x=\frac{24}{8}$

$x=3$

Thus the solution of this system of equations is x=3 and y=3

Answer 2

$\left \{ {{4x+2y=18(1)} \atop {2x+3y=15(2)}} \right.$
Lets multiply equation (2) by -2 to get:
$-4x-6y=-30$

Now we can add equations (1) and (2) to eliminate x:
$\left \{ {{4x+2y=18}+ \atop {-4x-6y=-30}} \right.$
$-4y=-12$
$y= \frac{-12}{-4}$
$y=3$
Now that we know the value of y, we can replace it in equation (1) to get the value of x:
$4x+2(3)=18$
$4x+6=18$
$4x=12$
$x= \frac{12}{3}$
$x=3$

We can conclude that both x and y are equal to 3.