Pleeeese help!
Use the substitution method to solve each linear system:
-x+3y+1=0
3x-y+1=0
4x-3y=-13
-2x+y=4
Please help, thanks:):)!!!!
1)
x= -.5
y= -.5
2)
x=.5
y=5
1.
from the 1st equation: x = 3y+1
into the 2nd:
3(3y+1) - y +1 = 0
9y + 3 - y +1 = 0
8y = -4
y = -1/2
sub into 2nd:
3x - (-1/2) + 1 = 0
3x = -3/2
x = -1/2
Do #2 the same way
from the 2nd: y = 2x+4
etc
(Just stating the answers is not acceptable and serves no purpose)
Oh thank you to both helpers!!! I have understood how to do it now:)
Sure, I can help you solve these systems of linear equations using the substitution method. The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation.
For the first system:
1. Solve the first equation for one variable. Let's solve it for x:
-x + 3y + 1 = 0
Add x to both sides:
3y + 1 = x
2. Substitute this expression for x in the second equation:
3x - y + 1 = 0
Replace x with 3y + 1:
3(3y + 1) - y + 1 = 0
Simplify by distributing:
9y + 3 - y + 1 = 0
Combine like terms:
8y + 4 = 0
3. Solve for y:
Subtract 4 from both sides:
8y = -4
Divide both sides by 8:
y = -4/8
y = -1/2
4. Substitute this value of y back into the first equation to find x:
-x + 3(-1/2) + 1 = 0
Simplify:
-x - 3/2 + 1 = 0
-x - 3/2 + 2/2 = 0
-x - 1/2 = 0
Add x to both sides:
-1/2 = x
x = -1/2
So, the solution to the first system is x = -1/2 and y = -1/2.
Now let's move on to the second system:
1. Solve the first equation for one variable. Let's solve it for y:
4x - 3y = -13
Subtract 4x from both sides:
-3y = -4x - 13
2. Divide both sides by -3:
y = (4/3)x + 13/3
3. Substitute this expression for y in the second equation:
-2x + y = 4
Replace y with (4/3)x + 13/3:
-2x + (4/3)x + 13/3 = 4
Combine like terms:
(-6/3)x + (4/3)x + 13/3 = 4
(-2/3)x + 13/3 = 4
4. Subtract 13/3 from both sides:
(-2/3)x = 4 - 13/3
Simplify the right side:
(-2/3)x = 12/3 - 13/3
= -1/3
5. Multiply both sides by -3/2:
x = (-1/3)(-3/2)
= 1/2
6. Substitute this value of x back into the expression for y:
y = (4/3)(1/2) + 13/3
= 2/3 + 13/3
= 15/3
= 5
So, the solution to the second system is x = 1/2 and y = 5.
I hope that helps! Let me know if you have any other questions.