How do you solve 2x + y = 5 and y = 3x + 2 using substitution?

2 Answers
Jul 30, 2016

x=3/5
y=19/5

Explanation:

2x+y=5
Putting y=3x+2 in the above equation we get
2x+3x+2=5
or
5x+2=5
or
5x=5-2
or
5x=3
or
x=3/5=======Ans 1
By putting x=3/5 in the equation y=3x+2
we get
y=3(3/5)+2
or
y=9/5+2
or
y=(9+2(5))/5
or
y=(9+10)/5
or
y=19/5=====Ans 2

Jul 30, 2016

x = 3/5, y = 3 4/5

Explanation:

This type of question is particularly common when working with straight lines.

Note that there is a single y term in both equations.

y = -2x+5" and " y = 3x +2

At the point where the two lines intersect, the x- and y- values are equal.

If " y = y" " it follows that:

3x +2 =-2x+5

5x = 3

x = 3/5

There are now two equations to find a value for y. If we get the same answer for each we will know our answers are correct.

y = 3xx 3/5 +2 = 3 4/5" "y = -2 xx3/5 +5 = 3 4/5