SOLUTION: Solve each system of equations using the substitution method. 1)4x+y=160 12x-13y=-160

Question 26479: Solve each system of equations using the substitution method.

1)4x+y=160
12x-13y=-160

Found 2 solutions by elima, algebrawiz:
Answer by elima(1433) (Show Source): You can put this solution on YOUR website!
First solve one of the equations for one of the variables;
Lets solve the first equation for y;
4x+y=160
y=160-4x
Now substitute that into the next equation for y;
12x-13(160-4x)=-160
12x-2080+52x=-160
12x+52x=-160+2080
64x=1920
x=30
Now that we have what x= lets find y;
4(30)+y=160
120+y=160
y=160-120
y=40
Hope you understand
=)
Answer by algebrawiz(2) (Show Source): You can put this solution on YOUR website!
Ok, lets go through the steps.
1.You need to solve the equation for x or y. Using the first equation(4x+y=16) lets solve for y.

a. 4x + y = 16
b. subtract 4x from both sides
c. we get y =-4x + 16
2.Now we can use this information to solve the problem by substituting -4x+16 into y for the second equation (12x-13y=-160). Lets do this:

a. 12x - 13y = -160
b. 12x - 13(-4x+16) = -160 plug -4x+16 in for y
c 12x - (-52x+208) = -160 distribute the 13 (notice I put the answer in parentheses so that I can distribute the - sign.)

d. 12x + 52x - 208 = -160 distibute the - sign
e. 64x - 208 = -160 combine like terms (x), now solve for x
f. add 208 to both sides
g. 64x = 48 next divide both sides by 64

h. x= 48/64 = .75 since we know y=-4x+16 lets plug in x to find y
i.y= -4(.75)+16 do the math
y=13 so the answer is x=.75 and y= 13
The best part of algebra is that you can check the solution by pluging it back into the problem. Remember it must be true for both of the ORIGINAL equation
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