Can some please help me work out each of these systems?
1. 4y=13+2x
6x+4y=9
2. Y=6-2x
5x=14-3y
3. 4x-6y=15
6x=10+4y
since I just showed you how to do three others just like these, do you have any ideas on these?
elimination or substitution will work fine.
Please help me I don't get how to move the equation around. At least just set up the equation for me.
for elimination, you want all the equations to look the same, so it's easy to add/subtract. The usual way is to give them the form
ax+by = c
So, for #1, we have
4y=13+2x
6x+4y=9
On the first one, subtract 2x from each side and you have
-2x+4y = 13
the 2nd is ok, so you now have
-2x+4y = 13
6x+4y = 9
If you subtract, the y's go away and you have
-8x = 4
x = -1/2
Now you can plug that into either equation to find y.
For substitution, isolate one variable and substitute into the other equation. For #2, we have
y=6-2x
5x=14-3y
The first equation already shows us what y must be, so put it into the second equation to get
5x = 14-3(6-2x)
5x = 14-18+6x
-x = -4
x = 4
now use that to get y.
Go ahead and try either method on the 3rd problem and if you get stuck, come on back for further pointers.
Certainly! Let's work through each system of equations step-by-step:
1. 4y = 13 + 2x
6x + 4y = 9
To solve this system, we can use the method of substitution. We want to solve for either x or y in one equation, and then substitute that expression into the other equation. Let's solve for y in the first equation:
4y = 13 + 2x
Divide both sides by 4:
y = (13 + 2x) / 4
Now we substitute this expression for y in the second equation:
6x + 4((13 + 2x) / 4) = 9
Multiply 4 to both sides:
6x + 13 + 2x = 9
Combine like terms:
8x + 13 = 9
Subtract 13 from both sides:
8x = -4
Divide both sides by 8:
x = -4/8
Simplify:
x = -1/2
Now that we have the value of x, we can substitute it back into the first equation to solve for y:
4y = 13 + 2(-1/2)
4y = 13 - 1
4y = 12
Divide both sides by 4:
y = 3
Therefore, the solution to this system of equations is x = -1/2 and y = 3.
2. y = 6 - 2x
5x = 14 - 3y
Again, let's use the substitution method. Let's solve for y in the first equation:
y = 6 - 2x
Now substitute this expression for y in the second equation:
5x = 14 - 3(6 - 2x)
Distribute the -3 to both terms inside the parentheses:
5x = 14 - 18 + 6x
Combine like terms:
5x - 6x = 14 - 18
-x = -4
Multiply both sides by -1:
x = 4
Now substitute this value of x back into the first equation:
y = 6 - 2(4)
y = 6 - 8
y = -2
The solution to this system of equations is x = 4 and y = -2.
3. 4x - 6y = 15
6x = 10 + 4y
We'll use the substitution method again. Let's solve for 6x in the second equation:
6x = 10 + 4y
Now substitute this expression for 6x in the first equation:
4(10 + 4y) - 6y = 15
Distribute the 4 to both terms inside the parentheses:
40 + 16y - 6y = 15
Combine like terms:
10y + 40 = 15
Subtract 40 from both sides:
10y = -25
Divide both sides by 10:
y = -2.5
Now substitute this value of y back into the second equation:
6x = 10 + 4(-2.5)
6x = 10 - 10
6x = 0
Divide both sides by 6:
x = 0
The solution to this system of equations is x = 0 and y = -2.5.
I hope this helps! Let me know if you have any further questions.