solve the system of equations
5x+2y=11 3x-4y=4 give answer as decimal if required. any help would be appreciated, thank you
multiply the top equation by 2 and you have
10x+4y = 22
3x-4y = 4
now add, and the y's go away, leaving
13x = 26
Now you can find x, then y.
still having trouble getting y. why multiply top by 2. first time doing this, sorry thanks for the help
this is called elimination. You try to make one variable disappear, then you can find the other one.
Since one equation had 2y and the other had 4y, you multiply one by 2, so you get 4y in both equations. Then when you add 4y and -4y, you get
13x + 0y = 26
and y is gone. Now x=2, and you can use either equation to find y:
5*2+2y=11 so y = 1/2
or
3*2-4y=4 so y = 1/2
You can also use substitution. Rearranging the 1st equation gives
2y = 11-5x
Since 4 = 2*2, you can plug that into the 2nd equation to have
3x-2(11-5x) = 4
3x-22+10x = 4
13x = 26
x=2
as before.
steve, thank you so much for explaining this. I get it now.
To solve the system of equations:
Step 1: Choose one equation of the system and solve it for one variable in terms of the other variable. Let's choose the first equation.
5x + 2y = 11
Solve for x:
5x = 11 - 2y
Divide both sides of the equation by 5:
x = (11 - 2y) / 5
Step 2: Substitute the expression for x from Step 1 into the second equation of the system.
3x - 4y = 4
Substitute x with (11 - 2y) / 5:
3((11 - 2y) / 5) - 4y = 4
Simplify the equation:
(33 - 6y) / 5 - 4y = 4
Multiply both sides of the equation by 5 to eliminate the denominator:
33 - 6y - 20y = 20
Combine like terms:
-26y = -13
Step 3: Solve the equation obtained in Step 2 for y.
Divide both sides of the equation by -26:
y = -13 / -26
Simplify:
y = 1/2
Step 4: Substitute the value of y back into either equation to solve for x. Let's use the first equation.
5x + 2(1/2) = 11
5x + 1 = 11
Subtract 1 from both sides:
5x = 10
Divide both sides of the equation by 5:
x = 10 / 5
Simplify:
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 1/2.