Solve 4x+6y=21 7x-3y=3
well, you can see from the 2nd equation that 3y=7x-3. So, 6y=14x-6
Plug that into the 1st equation to find x, and then you can get y.
Or, equivalently, multiply the 2nd by two and then you have
4x+6y = 21
14x-6y = 6
Now just add the two equations and y vanishes, leaving
18x=27
...
Please explain further
Thank u so much. This page helps me a lot
To solve the system of equations:
4x + 6y = 21
7x - 3y = 3
There are several methods to solve a system of equations, such as substitution, elimination, or using matrices. Let's solve it using the method of elimination.
Step 1: Multiply both sides of the second equation by 2 to make the coefficients of the y term in both equations equal:
4x + 6y = 21
14x - 6y = 6
Step 2: Add the two equations together:
(4x + 6y) + (14x - 6y) = 21 + 6
18x = 27
Step 3: Divide both sides of the equation by 18 to solve for x:
18x / 18 = 27 / 18
x = 3/2 = 1.5
Step 4: Substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
4(1.5) + 6y = 21
6 + 6y = 21
6y = 21 - 6
6y = 15
Step 5: Divide both sides of the equation by 6 to solve for y:
6y / 6 = 15 / 6
y = 15/6 = 2.5
Therefore, the solution to the system of equations is x = 1.5 and y = 2.5.