Find m and a:
12x + 3y = 36
mx - 9y = a
Put the equation in standard form which would be y=4x+ 12
^ ^
m a
how do you find m and a once you put the first term in standard form?
3 y = -12 x + 36
so
y = -4 x + 12
or
y = (-4) x + 12
that looks like
y = m x + b
so
m = -4 and b = 12
To find the values of m and a, we need to use the system of equations given.
First, let's rearrange the equations in the standard form (Ax + By = C) to make it easier to work with:
Equation 1: 12x + 3y = 36
Equation 2: mx - 9y = a
To solve this system of equations, we have a few options. One method is to use the method of substitution. Here are the steps:
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve Equation 2 for x:
mx - 9y = a
mx = 9y + a
x = (9y + a) / m
Step 2: Substitute the expression for x into the other equation and solve for y. Substitute (9y + a) / m for x in Equation 1:
12((9y + a) / m) + 3y = 36
Step 3: Solve the equation for y. Let's simplify Equation 1:
(108y + 12a) / m + 3y = 36
(108y + 12a + 3my) / m = 36
108y + 12a + 3my = 36m
108y + 12a = 36m - 3my
108y + 12a = 36m (since we can divide through by y)
36y + 4a = 12m
Step 4: Now we have a new equation with only y and a. We can solve for y:
36y + 4a = 12m
36y = 12m - 4a
y = (12m - 4a) / 36
y = (m - (2a/3)) / 3
Step 5: Now we substitute the value of y in terms of m and a into Equation 2:
mx - 9((m - (2a/3)) / 3) = a
Step 6: Simplify Equation 2:
mx - (3m - 2a)/3 = a
3mx - 3m + 2a = 3a
3mx - 3m = a - 2a
3mx - 3m = -a
Step 7: Now we have an equation with only m and a. We can solve for m:
3mx - 3m = -a
m(3x - 3) = -a
m = -a / (3x - 3)
Therefore, the value of m is -a / (3x - 3) and the value of a is arbitrary, since it does not depend on any other variable.