How to subsitute y=2x-3 and y=-x+3

Question

I have trouble with algebra.

Answer 1

You have two expressions that are defined by y.  Just equate those expressions.

 

2x - 3 = -x + 3

 

 

Now we can solve for x from this equation.

 

Add x on both sides of the equation.

 

3x - 3 = 3

 

 

Add 3 on both sides of the equation.

 

3x = 6

 

 

Divide both sides of the equation by 3.

 

x = 2

 

 

Next, substitute this value of x to find y.   Since we set the expressions equal to each other, the y values will be the same.

 

Therefore,

 

y = -2 + 3

y = 1

 

 

Answer 2

Substitution means that we have a value of a variable, and we use that in the equation.

y = 2x - 3

y = -x + 3

 

The interesting thing here is that both of these equations equal y, so that means that they equal one another:

2x - 3 = -x + 3

 

So now we need to isolate x. Start by adding x to both sides:

2x - 3 + x = -x + 3 + x

3x - 3 = 3

 

Now move the constants to the other side:

3x - 3  + 3 = 3 + 3

3x = 6

 

Divide both sides by 3:

3x / 3 = 6 / 3

x = 2

 

Now that we have x, we can use that to find y in our equations and then check our answer:

y = 2 * 2 - 3

y = 4 - 3

y = 1

 

y = -2 + 3

y = 1