solve these similtanious equations using an algebraic method
4x+3y=21
2x+y=8
you must show your working
multiply the second equation by two..
4x + 2y=16
Now subtract that equation from the first.
To solve the simultaneous equations 4x + 3y = 21 and 2x + y = 8 using an algebraic method, you can follow the steps below:
Step 1: Multiply the second equation by 2 to eliminate the x term:
2(2x + y) = 2(8)
This gives you 4x + 2y = 16.
Step 2: Now subtract the equation 4x + 2y = 16 from the first equation, 4x + 3y = 21, to eliminate the x term:
(4x + 3y) - (4x + 2y) = 21 - 16
This simplifies to y = 5.
Step 3: Substitute the value of y (which we found to be 5) back into one of the original equations to solve for x. For convenience, let's use the second equation, 2x + y = 8:
2x + 5 = 8
Step 4: Subtract 5 from both sides of the equation:
2x + 5 - 5 = 8 - 5
This simplifies to 2x = 3.
Step 5: Divide both sides of the equation by 2 to solve for x:
(2x)/2 = 3/2
This gives x = 3/2 or x = 1.5.
Therefore, the solution to the simultaneous equations 4x + 3y = 21 and 2x + y = 8 is x = 1.5 and y = 5.