Can you pliz help me solve the following simultaneous equation 3x-y=2 and 3y+9x=4
3x-y=2 Multiplt it by 3
9x-3y=6 Add to it the other eq.
9x+3y=4 You get 18x=10 or x=5/9
Substitute in any eq.
3*5/9-y=2 or y=15/9-2=5/3 -2
or y=(5-6)/2=-1/6.
Check: 3*5/9-(-1/6)=2 or 5/3+1/6=2
or (10+2)/6=2 ok.
9*5/9-3*1/3=4 or 5-1=4 ok.
or ... using substitution
from the 1st: y = 3x-2
sub into the 2nd
3(3x-2) + 9x = 4
9x - 6 + 9x = 4
18x = 10
x = 5/9
back into the 1st:
y = 3(5/9) - 2
= 5/3 - 2
= -1/3
in original:
1st equation:
LS = 3(5/9) - (-1/3) = 6/3 = 2 = RS
2nd equation:
LS= 3(-1/3) + 9(5/9) = -1 + 5 = 4 = RS
So x = 5/9 and y = -1/3
Sure! I can help you solve the given system of simultaneous equations step-by-step.
Step 1: Let's solve the first equation for y.
3x - y = 2 (Equation 1)
-y = 2 - 3x (Rearrange the equation by subtracting 3x from both sides)
y = 3x - 2 (Multiply both sides by -1 to get y positive)
Step 2: Substitute the value of y from Equation 1 into the second equation.
3y + 9x = 4 (Equation 2)
3(3x - 2) + 9x = 4 (Substitute y = 3x - 2 into Equation 2)
Step 3: Simplify the equation.
9x - 6 + 9x = 4 (Multiply 3 by 3x and -2)
18x - 6 = 4 (Combine the terms with x)
18x = 4 + 6 (Add 6 to both sides)
18x = 10 (Combine the constants)
Step 4: Solve for x.
x = 10/18 (Divide both sides by 18 to isolate x)
Step 5: Simplify the result.
x = 5/9 (Simplify the fraction 10/18 to the lowest terms)
Step 6: Substitute the value of x back into Equation 1 to solve for y.
y = 3x - 2 (Equation 1)
y = 3(5/9) - 2 (Substitute x = 5/9 into Equation 1)
Step 7: Simplify the equation.
y = 15/9 - 2 (Multiply 3 by 5/9)
y = 5/3 - 6/3 (Find a common denominator)
y = -1/3 (Subtract the numerators and keep the denominator)
So, the solution to the given simultaneous equations is x = 5/9 and y = -1/3.
Of course! I'd be happy to help you solve the simultaneous equations.
To solve a system of equations, you can use different methods, such as substitution, elimination, or matrix methods. Let's solve this particular system of equations using the substitution method:
Step 1: Solve one equation for one variable (preferably one that can be easily isolated).
Let's solve the first equation (3x - y = 2) for y:
3x - y = 2
-y = -3x + 2
y = 3x - 2
Step 2: Substitute the expression for y in the second equation.
In the second equation (3y + 9x = 4), substitute y with 3x - 2:
3(3x - 2) + 9x = 4
9x - 6 + 9x = 4
18x - 6 = 4
Step 3: Solve the equation obtained in step 2 for x.
18x - 6 = 4
18x = 4 + 6
18x = 10
x = 10/18
x = 5/9
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Let's use the first equation (3x - y = 2) again:
3(5/9) - y = 2
15/9 - y = 2
-y = 2 - 15/9
-y = 18/9 - 15/9
-y = 3/9
y = -1/3
Therefore, the solution to the system of equations is x = 5/9 and y = -1/3.