Solve the system of equation. 5x+2y=7 and -2x+6y=9. Enter the y-coordinate of the solution.
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Let's call Maura's age now M and Cara's age now C.
We know Maura is five years younger than Cara. In symbols that is, M - 5 = C
We also know that 7 years ago Maura's age was half of Cara's. Maura's age 7 years ago was M-7 and Cara's age seven years ago was C-7. Since Maura's age (7 years ago) was half of Cara's we can write in symbols:
Let's take that last equation and substitute C - 5 for M (this is because according to our first equation these are equal). When we do this we get an equation with only C as the variable and solve for C as follows:
Cara is 17. Since Maura is 5 years younger she is 12.
As a check, seven years ago Cara was 10 and Maura was 5. It is the case that Maura was half Cara's age seven years ago.
We know Maura is five years younger than Cara. In symbols that is, M - 5 = C
We also know that 7 years ago Maura's age was half of Cara's. Maura's age 7 years ago was M-7 and Cara's age seven years ago was C-7. Since Maura's age (7 years ago) was half of Cara's we can write in symbols:
Let's take that last equation and substitute C - 5 for M (this is because according to our first equation these are equal). When we do this we get an equation with only C as the variable and solve for C as follows:
Cara is 17. Since Maura is 5 years younger she is 12.
As a check, seven years ago Cara was 10 and Maura was 5. It is the case that Maura was half Cara's age seven years ago.
Ok let's do this*pops knuckles*
let's add the first side
order of operations demands that we do multiplication first(P.E.M.D.A.S)
so
now we can add the 1 from
into our six
now we substract
now we have
now we focus on the
other side
since 5 is in paranthesis we use something called the distributive property. it mean we will multiply the 5 by both of the 2.
now we have
(the three is from the original equation)
now we plug in our final numbers
or
I hope this helps
let's add the first side
order of operations demands that we do multiplication first(P.E.M.D.A.S)
so
now we can add the 1 from
into our six
now we substract
now we have
now we focus on the
other side
since 5 is in paranthesis we use something called the distributive property. it mean we will multiply the 5 by both of the 2.
now we have
(the three is from the original equation)
now we plug in our final numbers
or
I hope this helps