Question

Solve each system of equation algebraically
y=x+2
y=-3x

Answer 1

Try this solution:

`\left \{ {{y=x+2} \atop {y=-3x}} \right. \ =\ \textgreater \ \ \left \{ {{-3x=x+2} \atop {y=x+2}} \right. \ =\ \textgreater \ \ \left \{ {{y=2- (1)/(2)} \atop {x=- (1)/(2)}} \right. \ =\ \textgreater \ \ \left \{ {{y= (3)/(2)} \atop {x=- (1)/(2)}} \right.`

Answer 2

The easiest method to use to solve this equation is substitution. This is because we already have our second equation set equal to the variable y, so we can substitute the x values in for the variable y in the first equation, as follows:

y = x + 2

y = -3x

-3x = x + 2

To simplify, we should subtract x from both sides of the equation so that we can have all of the x terms isolated on the left side of the equation.

-3x - x = x - x + 2

-4x = 2

Finally, we must divide both sides of the equation by -4 to get the variable x alone.

x = -2/4

Because both the numerator and denominator of this fraction are divisible by 2, we can use this knowledge to simplify the fraction by dividing by the GCF of 2.

x = -1/2

Now that we know the value of x, we can substitute this value into either of our original equations to find out the value of y.

y = -3x

y = -3(-1/2)

y = 3/2

Therefore, your answer is x = -1/2 and y = 3/2, or written as an ordered pair (-1/2, 3/2).

Hope this helps!