5x+2y=48 and 3x-2y=32

Question

Need help with the steps to solve this equations for x and y.

Answer 1

Hi Phyllis;

The first thing we need to notice is that 2y is in both equations.  This will make this very easy.

5x+2y=48

3x-2y=32

Let's add the two equations together...

8x=80

x=10

 

Let's plug-in x=10 into either equation to establish the value of y.  I randomly select the first...

5x+2y=48

[5(10)]+2y=48

50+2y=48

Let's subtract 50 from both sides...

-50+50+2y=48-50

2y=-2

Let's divide both sides by 2...

(2y)/2=-2/2

y=-1

Let's plug-in both values into the other equation to verify (10,-1)...

3x-2y=32

[3(10)]-[2(-1)]=32

30+2=32

32=32

The two lines intersect at the point of...

(10,-1)