To solve the simultaneous equations:
1) y + 2x - 1 = 0
2) 2y - 3x + 5 = 0
We can use the method of substitution or elimination.
Method 1: Substitution
From equation 1, let's solve for y in terms of x:
y = -2x + 1
Now, substitute this value of y into equation 2:
2(-2x + 1) - 3x + 5 = 0
Simplify the equation:
-4x + 2 - 3x + 5 = 0
-7x + 7 = 0
-7x = -7
x = 1
Substitute this value of x back into equation 1 to solve for y:
y = -2(1) + 1
y = -2 + 1
y = -1
Therefore, the solution to the simultaneous equations is x = 1 and y = -1.
Method 2: Elimination
Multiply equation 1 by 2 and equation 2 by 3 to make the coefficients of x in both equations equal:
2(y + 2x - 1) = 0
3(2y - 3x + 5) = 0
Simplify the equations:
2y + 4x - 2 = 0
6y - 9x + 15 = 0
Now, we can combine these equations by adding them together:
(2y + 6y) + (4x - 9x) - (2 + 15) = 0
8y - 5x - 17 = 0
Rearrange this equation to isolate y:
8y = 5x + 17
y = (5/8)x + 17/8
So, we have derived the equation of a straight line that describes y in terms of x. This line has the same solution as the original simultaneous equations.
Therefore, there are infinitely many solutions to this system of equations, represented by the equation y = (5/8)x + 17/8.
Solve the two linear simultaneous equation, y + 2x -1=0 and 2y - 3x + 5=0
1 answer
1 answer