solve using the substitution method....(solutions must be in ordered pairs form)
9m+n=24
m-8n=27
9m+n=24
m-8n=27
n= 24-9m
27= m - 8(24-9m)
27= m - 192 - 72m
219= -71m so m = 3.0845
Double check by entering this into the other equation. 9(-3.0845)+ (24-9(-3.0845)
-27.7605 + 24 - -27.7605 = 24.
so m = -3.0845
-3.0845 - 8(n)= 27
-8n= 30.0845
n= - 3.7606
m: -3.0845
n= -3.7606
rearrange the second to
m = 8n+27
sub that back into the first
8(8n+27) = 24
64n + 216 = 24
64n = -192
n = -3
I am sure you can finish it.
okay, so you have(1) 9m+n=24 and (2) m-8n=27
i'm going to use isolate the m in the second formula, that way you can enter it into the first.
m-8n=27
isolate the m by moving the other numbers to the other side
m=27+8n
^substitute that number for m
9(27+8n)+n=24 solve.
243+72n+n=24 collect like terms.
243+73n=24 isolate the n by subtracting
-243 -243
73n=-219 divide -219 by 73 to isolate the n
n=-3
how substitute n into any of the 2 formulas to find m
I'll use the 2nd formula, but either would work.
so, m-8n=27 substitute the n=-3
m-8(-3)=27, multiply -8(-3)
m+24=27, isolate m
-24
m=27-24
m=3
G=F+2E, FOR F
To solve the system of equations using the substitution method, we need to isolate one of the variables in one equation and substitute it into the other equation. Let's solve the system step by step:
Step 1: Solve one equation for one variable
Let's solve the second equation for m:
m - 8n = 27
We can rearrange the equation by adding 8n to both sides:
m = 27 + 8n
Step 2: Substitute the value of m into the other equation
Now, substitute the value of m from the second equation into the first equation:
9m + n = 24
Replacing m with 27 + 8n, we have:
9(27 + 8n) + n = 24
Step 3: Simplify and solve for n
Expand the expression using the distributive property:
243 + 72n + n = 24
Combine like terms:
73n + 243 = 24
Subtract 243 from both sides:
73n = 24 - 243
73n = -219
Divide both sides by 73:
n = -219 / 73
n = -3
Step 4: Solve for m
Now, substitute the value of n back into the second equation to solve for m:
m - 8n = 27
m - 8(-3) = 27
m + 24 = 27
Subtract 24 from both sides:
m = 27 - 24
m = 3
Therefore, the solution to the system of equations in ordered pair form is (m, n) = (3, -3).