1.Sally age is 12 years plus half her age. How old is she?
2.Given that: 4x-y+9=0 and 3y-2x=7, solve for x.
I'll answer 2.
to get rid of the y's we make this a simultaneous equation
(1)4x-y=-9
(2)3Y-2X=7
the number of y's must be equal so that they will cancel eachother out when we add them together
so 3*(1)=12x-3y=-27
then we do (1)+(2)
12x-3y+3y-2x=-27+7
hopefully you will see that the y's cancel eachother out and we are left with
10x=-20
therefor x=-2
if you are unsure with any of the steps feel free to ask :)
gau
1. To find Sally's age, we can represent it as an algebraic expression. Let's call Sally's age "x". The problem states that Sally's age is 12 years plus half her age, which can be written as:
x = 12 + (1/2)x
To solve for x, we can simplify the equation:
(1/2)x = 12
To isolate x, we can multiply both sides of the equation by 2:
x = 24
So Sally is 24 years old.
2. To solve the system of equations 4x - y + 9 = 0 and 3y - 2x = 7, we can use the method of substitution or elimination.
Method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we have:
y = 4x + 9
Step 2: Substitute the expression obtained in step 1 into the other equation.
Now substitute the expression for y in the second equation:
3(4x + 9) - 2x = 7
Step 3: Simplify and solve for x.
Distribute 3 to 4x and 9:
12x + 27 - 2x = 7
Combine like terms:
10x + 27 = 7
Subtract 27 from both sides:
10x = -20
Divide both sides by 10:
x = -2
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the first equation:
4(-2) - y + 9 = 0
Simplify:
-8 - y + 9 = 0
Combine like terms:
-y + 1 = 0
Subtract 1 from both sides:
-y = -1
Multiply both sides by -1:
y = 1
Therefore, the solution to the system of equations is x = -2 and y = 1.