5x -2y = 7
The coefficient of y in Equation 1 is 1. So first we make y the subject of Equation 1:
y =
13 - 3xNext, substitute this expression for y in Equation 2 and solve for x:
| 5x - 2(13 - 3x) = 7 | Multiply out bracket |
| 5x - 26 + 6x = 7 | Combine like terms (x's on one side, numbers on the other) |
| 11x = 33 | Divide both sides by 11 to solve for x |
| x = 3 |
Finally, substitute the solution for x into the expression for y:
y = 13 - 3(3) = 4
y = 4
So the solution to the pair of simultaenous linear equations is (3,4).
2x + y = 4
The coefficient of y in Equation 2 is 1. So first we make y the subject of Equation 2:
y =
4 - 2xNext, substitute this expression for y in Equation 1 and solve for x:
| 2x + 4(4 - 2x) = 10 | Multiply out bracket |
| 2x + 16 - 8x = 10 | Combine like terms (x's on one side, numbers on the other) |
| -6x = -6 | Divide both sides by -6 to solve for x |
| x = 1 |
Finally, substitute the solution for x into the expression for y:
y = 4 - 2(1) = 2
y = 2
So the solution to the pair of simultaenous linear equations is (1,2).
2x -4y = 8
The coefficient of x in Equation 1 is 1. So first we make x the subject of Equation 1:
x =
7 + 5yNext, substitute this expression for x in Equation 2 and solve for y:
| 2(7 + 5y) - 4y = 8 | Multiply out bracket |
| 14 + 10y - 4y = 8 | Combine like terms (y's on one side, numbers on the other) |
| 6y = -6 | Divide both sides by 6 to solve for y |
| y = -1 |
Finally, substitute the solution for y into the expression for x:
x = 7 + 5(-1) = 2
x = 2
So the solution to the pair of simultaenous linear equations is (2,-1).
x + 8y = 30
The coefficient of x in Equation 2 is 1. So first we make x the subject of Equation 2:
x =
30 - 8yNext, substitute this expression for x in Equation 1 and solve for y:
| 2(30 - 8y) + 4y = 12 | Multiply out bracket |
| 60 - 16y + 4y = 12 | Combine like terms (y's on one side, numbers on the other) |
| -12y = -48 | Divide both sides by -12 to solve for y |
| y = 4 |
Finally, substitute the solution for y into the expression for x:
x = 30 - 8(4) = -2
x = -2
So the solution to the pair of simultaenous linear equations is (-2,2).
-4x+5y = -26
None of the coefficients are 1. So we can choose to make any variable the subject.
Lets make x the subject of Equation 1:
x =
(10 + 4y)/2x = 5 + 2y
Next, substitute this expression for x in Equation 2 and solve for y:
-4(
5 + 2y ) + 5y = -26-20 - 8y + 5y = -26
-3y = -6
y = 2
Finally, substitute the solution for y into the expression for x:
x = 5 + 2(2) = 9
x = 9
So the solution to the pair of simultaenous linear equations is (9,2).
10x - 3y = 12
None of the coefficients are 1. So we can choose to make any variable the subject.
Lets make y the subject of Equation 2:
y =
(12-10x)/(-3)y = -4 + (10/3) x
Next, substitute this expression for y in Equation 1 and solve for x:
6x + 2(
-4 + (10/3) x) = 106x - 8 + (20/3) x = 10
(38/3) x = 18
x = 18*(3/38) = 27/19
Finally, substitute the solution for x into the expression for y:
y = -4 + (10/3)/(27/19) = -4 + 270/57 = -228/57 = 270/57 = 42/57 = 14/19
So the solution to the pair of simultaenous linear equations is (27/19,5/19).
