What is the value of x + y in the solution to the system of equations below?
x + 8y = 2
y = -0.25x
I just need the best explanation so i can do all my other problems cause im confused.
multiply the second equation by 4
4y=-x or x+4y=0
so now you have
x+8y=2
x+4y=0
subtract the second equation from the first.
4y=2
y=1/2 then solve for x
x+4y=0 or x=-2
With substitution:
x + 8(-.025x) = 2
x + -.2x = 2
.8x = 2
x = 2/.8 = 2.5
x + 8y = 2
y = -0.25x
Substitute.
x + 8(-0.25x) = 2
x - 2 = 2
x = 4
Wow: three answers. Edgard, recommend you do some checking of the answers, that checking will teach you some algebra.
Ms Sue, yours should read:
x-2x=2
x=-2
Dr M: you didn't multipy .25 correctly...
Thanks, Bobpursley. I goofed!
To find the value of x + y in the solution to the system of equations, we need to first solve the system. Here's how you can do it step by step:
1. Start with the two equations:
x + 8y = 2 (Equation 1)
y = -0.25x (Equation 2)
2. Since Equation 2 already expresses y in terms of x, we can substitute this expression into Equation 1. Replace y in Equation 1 with -0.25x:
x + 8(-0.25x) = 2
3. Simplify the equation by distributing 8 through -0.25x:
x - 2x = 2
4. Combine like terms on the left side of the equation:
-x = 2
5. To isolate x, multiply both sides of the equation by -1:
x = -2
6. Now that we have found the value of x, we can substitute it back into either equation to find the value of y. Let's use Equation 2:
y = -0.25(-2)
y = 0.5
7. So, the solution to the system of equations is x = -2 and y = 0.5.
8. Finally, to find the value of x + y, simply substitute the values we found into the expression:
(-2) + (0.5) = -1.5
Therefore, the value of x + y in the solution to the system of equations is -1.5.