How do you solve 5x+2y=12 and -6x-2y=-14?

1 Answer
Jan 21, 2016

{(x=2),(y=1):}

Explanation:

{(5x+2y=12" S1"),(-6x-2y=-14" S2"):}

Looking at the equation we can see that in S1 we have ay and in S2 we have -ay, thus we could use the Linear Systems with Addition or Subtraction to transform the system as :

{(S1),(S1+S2):}

{(5x+2y=12),(-x+0y=-2):}=>{(5x+2y=12),(x=2):}

Now you can put the x value in S1 to find the y value

{(5*2+2y=12),(x=2):}=>{(10+2y=12),(x=2):}=>{(5x+2y=12),(x=2):}

=>{(2y=12-10),(x=2):}=>{(y=cancel(2)^1/cancel(2)^1),(x=2):}

=>{(x=2),(y=1):}

graph{(5x+2y-12)(-6x-2y+14)=0 [-1.413, 5.518, -1.016, 2.45]}