Question 845824: Need help solving ASAP! Use the substitution method to solve the system of equations.
4(x - 2) = 8(y - 1)
16y - 32 = 2x + 4 Found 2 solutions by josgarithmetic, pmesler:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! Pick an equation. Solve for one variable in terms of the other variable. Substitute the formula of this solved variable into the other equation; and solve the single variable. Now, use the value found to solve for the second unknown variable.
That was WHAT to do but not showing any steps. Can you follow that and solve the two equations for x and y?
I would pick the second equation, SIMPLIFY it, and solve for x in terms of y. Then, substitute the formula for x into the first equation and solve for the value of y. Notice you now also have a formula for x. Use it with your newly found value of y and compute the value of x.
You can put this solution on YOUR website! This one was fun. The key to solving this is to simplify first. Let's start off by labeling the different equations as equations 1 and 2
1) 4(x - 2) = 8(y - 1)
2) 16y - 32 = 2x + 4
The first thing you want to do is simplify equation 1 by using the distributive property to simplify both sides of the equation.
So equation 1 looks like this after using the distributive property:
4x-8 = 8y-8
Now, once we have this simplified we want to simplify it even more. Let's try to get the y alone. We do that by dividing both sides by 8 to get this:
1/2x-8 = y-8
Now we just add 8 to both sides to get y by itself and we get this:
y = 1/2x.
So now we can express y in terms of x. Now let's use that knowledge to solve for equation 2
Equation 2 says
16y - 32 = 2x + 4.
Now all you need to do is substitute what we know y is into the equation and solve for x since we can now express y in terms of x.
16(1/2x) - 32 = 2x + 4. Now, solve for x.
Equation 2 becomes
8x - 32 = 2x + 4.
Subtract 2x from both sides
6x - 32 = 4
Add 32 to both sides.
6x = 36
Divide each side by 6.
x = 6
And since we know that y =1/2x that means y = 3.
Now plug in the values of x and y into the original equations to see of they check out.
4(6-2) = 8(3-1)
4(4) = 8(2)
16 = 16. Everything checks out for equation 1 so let's try equation 2
16(3)-32 = 2(6) + 4
48 - 32 = 12 + 4
16 = 16. Equation 2 checks out so the solution is (6,3).
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