solve each system of equation by elimination:
a. 3x-4=y, 3x=y+6
b. 2x=y+1, y=6-3x
c. x=5y+5, 3x=7-y
Thank you :))
3 x - y = 4
3 x - y = 6
never cross -parallel, no solution
2 x - y = 1
3 x + y = 6
--------------add
5 x = 7
x = 7/5 etc
1 x - 5 y = 5
3 x + 1 y = 7
multiply first by 3
3 x -15 y = 15
3 x + 1 y = 7
---------------subtract
-16 y = 8
y = -1/2 etc
what is the y of b and the x of c ?
y of b is 6-3x
x of c is 5y+5
surely you can evaluate those, given the other values!
a. To solve this system of equations by elimination, we can eliminate the variable "y" by adding the two equations together. Let's perform the elimination process:
Given equations:
1) 3x - 4 = y
2) 3x = y + 6
Step 1: Rearrange equation 2) to have "y" on the left side:
2) y = 3x - 6
Step 2: Substitute equation 2) into equation 1) to eliminate the variable "y":
1) 3x - 4 = 3x - 6
Step 3: Simplify and solve for "x":
3x - 4 = 3x - 6
Subtract 3x from both sides:
-4 = -6
Since the equation -4 = -6 is not true, this system of equations has no solution. The lines represented by these equations are parallel and will never intersect.
b. Let's solve this system of equations by elimination:
Given equations:
1) 2x = y + 1
2) y = 6 - 3x
Step 1: Rearrange equation 2) to have "y" on the right side:
2) y + 3x = 6
Step 2: Substitute equation 2) into equation 1) to eliminate the variable "y":
1) 2x = (6 - 3x) + 1
Step 3: Simplify and solve for "x":
2x = 7 - 3x
Add 3x to both sides:
5x = 7
Divide both sides by 5:
x = 7/5
Step 4: Substitute the value of "x" back into equation 2) to solve for "y":
y = 6 - 3(7/5)
y = 6 - 21/5
y = 30/5 - 21/5
y = 9/5
So the solution to this system of equations is x = 7/5 and y = 9/5 (or approximately x = 1.4 and y = 1.8).
c. Now, let's solve this system of equations by elimination:
Given equations:
1) x = 5y + 5
2) 3x = 7 - y
Step 1: Rearrange equation 2) to have "y" on the right side:
2) y + 3x = 7
Step 2: Multiply equation 1) by 3 to make the coefficients of "x" the same:
3x = 15y + 15
Step 3: Substitute equation 1) into equation 2) to eliminate the variable "x":
y + (15y + 15) = 7
Step 4: Simplify and solve for "y":
16y + 15 = 7
Subtract 15 from both sides:
16y = 7 - 15
16y = -8
Divide both sides by 16:
y = -8/16
y = -1/2
Step 5: Substitute the value of "y" back into equation 1) to solve for "x":
x = 5(-1/2) + 5
x = -5/2 + 10/2
x = 5/2
So the solution to this system of equations is x = 5/2 and y = -1/2 (or approximately x = 2.5 and y = -0.5).