please help, I have a test tomorrow and i don't get this.
solve by substitution
1. y = x - 3
x + y = 5
2. 5x + 2y = 0
x - 3y =0
if y=x-3, then you have to plug it into the equation.
for numb 1, y=x-3 so when you plug that in it makes the equation x+y=5 turns into x+x-3=5. then you solve by making the sides equal.
you do this by x+x-3=5
x-3=3
x=2
I'm with Zava on the idea, but I think one of us dropped a sign along the way. And I'm not at all sure it wasn't me, so I'll check at the end. Dropped signs happen all the time.
We have:
x + y = 5
but we're also given what y is: y = x - 3
So we can just replace y in the equation with (x-3)
x + y = 5
x + (x-3) = 5
2x - 3 = 5
2x = 5 + 3
2x = 8
x = 4
and since y = x -3
y = 4 - 3 = 1
Check:
y = x - 3
1 = 4 - 3 - OK
x + y = 5
4 + 1 = 5 - OK
The second one is a leetle trickiersince you''ll have to make one of the equations work for the substitution
x - 3y = 0
-> x = 3y --- that's the one we'll use!
5x + 2y = 0
5(3y) + 2y = 0
17y = 0 -> y = 0.
No that's not a mistake. The only answer is if x and y are both zero!
Sure, I can help you solve these equations using the substitution method.
1. y = x - 3
x + y = 5
To solve this system of equations, we can substitute the value of y from the first equation into the second equation. Since y = x - 3, we can replace y in the second equation with x - 3:
x + (x - 3) = 5
Now, we can combine like terms:
2x - 3 = 5
Next, we can isolate the x term by adding 3 to both sides:
2x = 8
Finally, we divide both sides by 2 to solve for x:
x = 4
To find the value of y, we substitute the value of x back into the first equation:
y = x - 3
y = 4 - 3
y = 1
So the solution to the system of equations is x = 4 and y = 1.
2. 5x + 2y = 0
x - 3y = 0
For this system of equations, we can solve it using substitution as well. From the second equation, we can express x in terms of y:
x = 3y
Now, we substitute this value of x into the first equation:
5(3y) + 2y = 0
Simplify the equation:
15y + 2y = 0
Combine like terms:
17y = 0
Now, we can solve for y by dividing both sides by 17:
y = 0
To find the value of x, we substitute the value of y back into the second equation:
x - 3y = 0
x - 3(0) = 0
x - 0 = 0
x = 0
So the solution to the system of equations is x = 0 and y = 0.