Solve
5x + 3y = 4
3x + 4y = 9
Just a bit confused
Please help
first one times 3
second one times 5
15 x + 9 y = 12
15 x + 20 y = 45
------------------subtract
0 x - 11 y = - 33
y= 3
then go back for x
5 x + 9 = 4
5 x = -5
x = -1
5x+3y=4 [eqn.1]
3x+4y=9[eqn.2]
now,
x=4-3y/5[eqn.3]
Now putting the value of x in eqn.2
3(4-3y/5)+4y=9
12-9y/5+4y=9
12-9y+20y/5=9
12+11y=45
11y=33
y=3
And x=4-3y/5
x=4-3*3/5
x=4-9/5
x=-1
To solve the system of equations
5x + 3y = 4 ----(1)
3x + 4y = 9 ----(2)
We can use the method of substitution or elimination. Let's solve it using the method of substitution.
Step 1: Solve equation (1) for x in terms of y.
Rearrange equation (1) to solve for x:
5x = 4 - 3y
Divide both sides of the equation by 5:
x = (4 - 3y)/5
Step 2: Substitute the value of x in equation (2) with the expression we obtained in step 1.
Substitute (4 - 3y)/5 for x in equation (2):
3(4 - 3y)/5 + 4y = 9
Multiply both sides of the equation by 5 to eliminate the fraction:
3(4 - 3y) + 20y = 45
Distribute the 3 on the left side:
12 - 9y + 20y = 45
Combine like terms:
11y + 12 = 45
Subtract 12 from both sides:
11y = 33
Divide both sides of the equation by 11:
y = 33/11
y = 3
Step 3: Substitute the value of y in equation (1) to find x.
Use equation (1) and substitute y with 3.
5x + 3(3) = 4
5x + 9 = 4
Subtract 9 from both sides:
5x = 4 - 9
5x = -5
Divide both sides by 5:
x = -1
So the solution to the system of equations is x = -1 and y = 3.
To solve this system of equations, you can use the method of substitution or elimination. I'll explain the steps for both methods, and you can choose the one you find more comfortable or understandable.
Method 1: Substitution
1. Start by solving one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:
5x + 3y = 4
Subtract 3y from both sides:
5x = 4 - 3y
Divide both sides by 5:
x = (4 - 3y)/5
2. Now, substitute the expression you obtained for x in the other equation:
3x + 4y = 9
Replace x with (4 - 3y)/5:
3((4 - 3y)/5) + 4y = 9
3. Simplify the equation by performing the necessary operations to eliminate the parentheses and simplify fractions.
4. Solve the equation obtained in step 3 to find the value of y.
5. Substitute the value of y back into one of the original equations to find the value of x.
6. Write the solution as an ordered pair (x, y).
Method 2: Elimination
1. Multiply one or both equations by suitable constants to make the coefficients of one variable identical or opposite in both equations.
2. Add or subtract the equations to eliminate one variable and solve for the remaining variable.
3. Substitute the value of the remaining variable back into one of the original equations to find the value of the variable you eliminated.
4. Write the solution as an ordered pair (x, y).
Choose one of these methods and apply the steps to solve the given system of equations.