Thread: equations system

ive been trying to answer these questions all night, 19 of them for homework and ive got 8 done. only 8 to go...

10. Solve the following systems of equations by substitution. Show your work.
a) y= 2x+10
y = 130

b) 2a + 3b = 35
b=10


c) 3x+5y = 12
x+3y=6



can someone explain to me how to do this, i dont understand it! i know how to check if their right afterwards, but especially for a.. i dont get what to 'plug in' and all that..

For 10a), you're told y = 130. Take that value and plug it in for y in the first equation, y = 2x + 10.

Replacing y by 130 gives 130 = 2x + 10. Solve for x by first subtracting 10 from both sides:

120 = 2x.

Now divide by 2; x = 60.

Same idea for 10b) -- They tell you b = 10, so plug 10 in wherever you see b in the first equation, then solve for a.

10c) is a little trickier.

Take the second equation, x + 3y = 6, and solve it for one of the variables. You can choose either one, but this is easier to solve for x, since x isn't being multiplied by anything. This gives: x = 6 - 3y.

Now that you know what x is (even though it's not a number, but still has y in it), take that and plug it in to the first equation. Wherever you see an "x", replace it by 6-3y, since they're the same thing.

Your first equation, 3x + 5y = 12, now becomes:

3(6-3y) + 5y = 12.

Distribute on the left:

18 - 9y + 5y = 12.

Combine like terms.

18 - 4y = 12.

Now solve for y, first by subtracting 18 from both sides:

-4y = -6

And now divide by -4:

y = 3/2.

Plug that value in to EITHER equation and solve for x. I'll plug it in to the second equation, x + 3y = 6.

This gives:

x + 3(3/2) = 6, so

x + 9/2 = 6.

subtract 9/2 from both sides (think of 6 as 12/2) to get

x = 3/2.

That gives your answer: x = 3/2 and y = 3/2. It's just a coincidence that they both are the same value.