solving a linear system: 3x - y = 15, x + 2y = -2

[BossanovaFiend]

How do you sovle this:

Use substitution to solve the linear system.

3x - y = 15
x + 2y = -2

 

[stapel]

How do you sovle this...?

You probably solve this using the substitution method they taught you! :wink:

You could probably most-easily solve the first equation for "y=" or the second equation for "x=". Then plug whichever you solved for into the other equation in place of that variable (that is, "substitute"), and solve for the value of the other value. Then back-solve for the first variable.

Please reply stating which equation you're solving for which variable, and show all the steps in how far you got after that point.

Thank you!

Eliz.

 

[BossanovaFiend]

3x - y = 15
x + 2y = -2

3x - y = 15
-3x -3x

y = -3x + 15

x + 2y = -2
x + 2(-3x + 15) = -2

x + -6x + 30 = -2
-5x + 30 = -2
-30 -30

-5x = -32
/-5 /-5

x = 6.4


y = -3x + 15
y = -3(6.4) + 15

y = -19.2 + 15
y = -4.2
x = 6.4

Thats how!! :shock:

 

[stapel]

3x - y = 15
x + 2y = -2

3x - y = 15
-3x -3x

y = -3x + 15

Sorry; no. If you subtract off the 3x, you're left with "-y = -3x + 15". The wrong sign throws off the rest, as can be confirmed by checking your solutions:

. . . . .3[6.4] - [-4.2] = 19.2 + 4.2 = 23.4

...not 15. But your method, in general, is correct. :wink:

Eliz.

 

[Mrspi]

How do you sovle this:

Use substitution to solve the linear system.

3x - y = 15
x + 2y = -2

Might be easier to solve the SECOND equation for x:

Subtract 2y from both sides of the second equation:

x + 2y - 2y = -2 - 2y
x = -2 - 2y

Now, substitute (-2 - 2y) for x in the first equation:

3x - y = 15

3(-2 - 2y) - y = 15

-6 - 6y - y = 15

Ok...take it from there. Find the value of y. Once you know what y is, then you can find x using the fact that x = -2 - 2y