hello i need help with system of equations theres 3 only thank you
2x+3y-17
3x+y=31
2(x-3y)=24
y=3x-2
2(x+4)=24
x+y=17
2x+3y=17 I assume
3x+y=31
try elimination
multiply the entire first equation by 3 to get 6x term
multiply the entire second equation by 2 to get 6x term
so:
6x+9y = 51
6x+2y = 62
----------- subtract
7 y = -11
y = -11/7
then 2x = 17+33/7
x = 152/14 = 76/7
check
3(76/7) -11/7 = 31, right
for the second one you already have y as a function of x so use substitution
2(x-3y)=24 ---> x - 3y = 12
y=(3x-2 )
x - 3(3x-2) = 12
-8 x + 6 = 12
-8 x = 6
x = -3/4 etc
are you sure whatb grade are you in
Of course! I'd be happy to help you with your system of equations. Let's solve each one step-by-step.
System of Equations 1:
2x + 3y = 17
3x + y = 31
To solve this system of equations, we can use the method of substitution or the method of elimination.
Method 1: Substitution:
1. Solve one of the equations for one variable in terms of the other.
For example, let's solve the second equation for y:
y = 31 - 3x
2. Substitute the value of y into the other equation.
Replace y in the first equation with 31 - 3x:
2x + 3(31 - 3x) = 17
3. Simplify and solve for x:
2x + 93 - 9x = 17
-7x + 93 = 17
-7x = 17 - 93
-7x = -76
x = -76 / -7
x ≈ 10.86
4. Substitute the value of x back into either of the original equations to solve for y.
Let's use the second equation:
3x + y = 31
3(10.86) + y = 31
32.58 + y = 31
y = 31 - 32.58
y ≈ -1.58
Therefore, the solution to System of Equations 1 is:
x ≈ 10.86 and y ≈ -1.58.
Now, let's proceed to the next system of equations:
System of Equations 2:
2(x - 3y) = 24
y = 3x - 2
1. Solve one equation for one variable.
In this case, we already have y expressed in terms of x in the second equation.
We don't need to do anything for now.
2. Substitute the expression of y from one equation into the other equation.
Replace y in the first equation with 3x - 2:
2(x - 3(3x - 2)) = 24
3. Simplify and solve for x:
2(x - 9x + 6) = 24
2(-8x + 6) = 24
-16x + 12 = 24
-16x = 24 - 12
-16x = 12
x = 12 / -16
x = -0.75
4. Substitute the value of x back into either of the original equations to solve for y.
Let's use the second equation:
y = 3x - 2
y = 3(-0.75) - 2
y = -2.25 - 2
y = -4.25
Therefore, the solution to System of Equations 2 is:
x = -0.75 and y = -4.25.
Lastly, let's solve the third system of equations:
System of Equations 3:
2(x + 4) = 24
x + y = 17
1. Simplify both equations:
2x + 8 = 24
x + y = 17
2. Solve the first equation for x:
2x = 24 - 8
2x = 16
x = 16 / 2
x = 8
3. Substitute the value of x into the second equation:
8 + y = 17
y = 17 - 8
y = 9
Therefore, the solution to System of Equations 3 is:
x = 8 and y = 9.
I hope this helps! Let me know if you have any further questions.