Could someone please help me.
Solve the linear equation by substitution.
Y=10-2.2x
5x+y=70
For the first equation I am getting x=21.4 and for the second equation I am getting y=-37. The answers are 21 3/7 and -37 1/7. Could you show me how you do this so I can see where I went wrong in my steps! Thank you
The first equation has y=10-2.2x
Substituting that value for y into the second equation:
5x + (10-2.2x)=70
5x + 10-2.2x=70
combining...
2.8x=60
x=?
Plug that value for x into the first equation to find y.
Cherie,
You are using decimals and rounding off your answer before you are substituting.
look at Quidditch's last line
2.8x = 60
x = 60/2.8 = 600/28 = 150/7 or 21 3/7
now y = 10 - 2.2(150/7)
= 10 - (22/10)(150/7)
= 10 - 330/7
= -260/7 or -37 1/7
since "anything"/7 is a repeating decimal, you will never get the "exact" answer by using decimals, you have to keep working in fractions
Of course, I'd be happy to help you with solving the linear equations by substitution. Let's go step by step to find the correct solutions.
The given equations are:
1) Y = 10 - 2.2x
2) 5x + y = 70
To start, we'll solve the first equation, Y = 10 - 2.2x, for Y in terms of x:
1) Y = 10 - 2.2x
Now, we'll substitute this expression for Y into the second equation, 5x + y = 70:
2) 5x + (10 - 2.2x) = 70
Now, let's simplify the equation:
5x + 10 - 2.2x = 70
Combine like terms:
2.8x + 10 = 70
Next, we'll isolate the variable x by subtracting 10 from both sides of the equation:
2.8x = 60
Now, divide both sides of the equation by 2.8 to solve for x:
x = 60 / 2.8
Evaluating this division gives us x ≈ 21.4286 (rounded to four decimal places).
Now that we have found the value of x, we need to substitute it back into one of the original equations to find the value of Y. Let's go back to the first equation:
Y = 10 - 2.2x
Substituting x = 21.4286:
Y = 10 - 2.2 * 21.4286
Calculating this gives us Y ≈ -37.1429 (rounded to four decimal places).
Therefore, the solutions to the system of equations are approximately x = 21.4286 and Y = -37.1429. However, if the desired answer is in the mixed fraction form, we can convert those decimal numbers into fraction form. For ease of reading, let's convert to mixed fraction form:
x = 21.4286 ≈ 21 3/7
Y = -37.1429 ≈ -37 1/7
So, the correct solutions are approximately x = 21 3/7 and Y = -37 1/7.
I hope this explanation helps you understand the process of solving linear equations by substitution. If you have any further questions, please feel free to ask!