Solve by the linear combination method (with or without multiplication).
x + y = 50
0.05x + 0.06y = 2.8
Eq1: X + Y = 50
Eq2: 0.05X + 0.06Y = 2.8
Multiply Eq1 by -0.05:
-0.05X - 0.05Y = -2.5
+0.05X + 0.06Y = 2.8
Add the Eqs:
0.01Y = 0.3,
Y = 30.
Substitute 30 for y in Eq1:
X + 30 = 50,
X = 20.
Solution Set = (20 , 30).
;
x+9y=14
-2+y=10
To solve the given system of equations using the linear combination method, we need to eliminate one variable by multiplying one or both equations by suitable constants and then adding or subtracting the equations to eliminate one variable at a time.
Let's start by multiplying the first equation by -0.06 and the second equation by 100 to eliminate the decimals:
-0.06(x + y) = -0.06(50)
0.05x + 0.06y = 2.8
which becomes:
-0.06x - 0.06y = -3
5x + 6y = 280
Now, we can add the two equations to eliminate x:
(-0.06x - 0.06y) + (5x + 6y) = -3 + 280
4.94x + 5.94y = 277
Now we have one equation with only y as the variable. Let's solve for y:
4.94x + 5.94y = 277
5.94y = 277 - 4.94x
y = (277 - 4.94x) / 5.94
This gives us the value of y in terms of x. We can substitute this value back into either of the original equations to solve for x.
Let's substitute y in the first equation:
x + (277 - 4.94x) / 5.94 = 50
Now, we can solve this equation to find the value of x. Once we have the value of x, we can substitute it back into the equation y = (277 - 4.94x) / 5.94 to find the value of y.
I hope this helps! Let me know if you have any further questions.