Solve the system of equations below.

Question

4x+y=16

2x+3y=-2

Answer 1

To solve a system of equations there are different ways to solve it

 

1st method

multiply one of the equations for a number and subtract the equations to have only one variable

this is : multiply the equation 2x+3y=-2 by 2 and you get

4x+6y=-4

 

subtract this new equivalent equation form the other one

    4x+y = 16

- (4x+6y=-4  )

 

y-6y =16 -(-4)  this is -5y=20  solving for y =-4

 

then you can use any equation to solve for x, let use 4x+y = 16,   this is 4x+ (-4) = 16

solve for x, 4x=16+4  then 4x=20 , x=5

 

The answer is  x,y =5,-4

 

 2nd Method

you can solve one variable from one equation and substitute the result in the other one.

 

If we take the first equation 4x+y=16 , and we solve for y=16-4x

then we substitute this in the second one:  

2x+3(16-4x)=-2 , then we have one equation with one one variable x and we can solve the equation and obtain the value of x

 

this is 2x + 48 -12x=-2  then -10x=-50,  this give us the same answer x= 5 and y =16-4(5) give us y =-4

The answer is x=5 and y=-4

 

best 

Carmen

 

Answer 2

Nanabah,

       In order to solve this system of simultaneous equations we will have to use elimination. 

 

In order to eliminate the variable x, we will multiply the bottom equation by 2, resulting in the equivalent equation

 

4x + 6y =- 4.

 

Our new system of equations is now

 

4x + y = 16

4x + 6y = -4

 

Now we will subtract the bottom equation from the top equation.

 

-5y =20

 

Next, we divide both sides of this equation by -5

 

y = -4

 

Now we will substitute y =-4 into the top equation and solve for x.

 

4x + (-4) = 16

 

Next, we will add 4 to both sides of the equation.

 

4x = 20

Now we divide both sides of the equation by 4.

 

x = 5

 

So the point where the graph of these two equations intersect is (5,-4)

 

Hope this helps.  :)

 

Gordon