How do you do this Simultaneous Equation?
3x+4y=14
x+y=3
Please give me the step by step solution.
Thanks a lot!
3x+4y=14 (1)
x+y=3 (2)
Multiply (2) by -3 to get the x's to cancel.
3x+4y=14 (1)
-3x-3y=-9 (3)
Add (1) and (3) together.
y=5
Replace y=5 in either original equation (1) or (2) to solve for x.
Now, I understand. Thanks, Jen!
To solve this system of simultaneous equations, you can use the method of substitution or the method of elimination. I will explain both methods, step by step.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable. In this case, let's solve the second equation for x in terms of y:
x + y = 3
x = 3 - y
Step 2: Substitute the expression for x (from step 1) into the other equation:
3x + 4y = 14
3(3 - y) + 4y = 14
Step 3: Simplify and solve for y:
9 - 3y + 4y = 14
y = 14 - 9
y = 5
Step 4: Substitute the value of y back into one of the original equations to solve for x:
x + 5 = 3
x = 3 - 5
x = -2
Therefore, the solution to the simultaneous equations is x = -2 and y = 5.
Method 2: Elimination
Step 1: Multiply either equation by a constant to make the coefficients of either x or y equal in magnitude but opposite in sign. In this case, let's multiply the second equation by 3 to make the coefficients of x equal:
3(x + y) = 3(3)
3x + 3y = 9
Step 2: Subtract this new equation from the first equation to eliminate x:
(3x + 4y) - (3x + 3y) = 14 - 9
4y - 3y = 5
y = 5
Step 3: Substitute the value of y into one of the original equations to solve for x:
x + 5 = 3
x = 3 - 5
x = -2
Therefore, the solution to the simultaneous equations is x = -2 and y = 5.