Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑚+3𝑛4m+3n==1919 (2)(2)𝑚m==𝑛−4n−4
Question
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑚+3𝑛4m+3n==1919 (2)(2)𝑚m==𝑛−4n−4
Solution
Sure, let's solve these equations step by step.
Given equations are:
(1) 4m + 3n = 19 (2) m = n - 4
Step 1: Substitute equation (2) into equation (1)
This gives us: 4(n - 4) + 3n = 19
Step 2: Simplify the equation
This gives us: 4n - 16 + 3n = 19
Step 3: Combine like terms
This gives us: 7n - 16 = 19
Step 4: Add 16 to both sides of the equation
This gives us: 7n = 35
Step 5: Divide both sides of the equation by 7
This gives us: n = 5
Step 6: Substitute n = 5 into equation (2)
This gives us: m = 5 - 4
Step 7: Simplify the equation
This gives us: m = 1
So, the solution to the system of equations is m = 1, n = 5.
Similar Questions
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑚+3𝑛4m+3n==3232 (2)(2)𝑚m==𝑛+1n+1
Identify if the following simultaneous equations are set up for the substitution method: (1)(1)2𝑝+3𝑞2p+3q==1717 (2)(2)𝑝p==𝑞+1q+1
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)2𝑟−𝑡2r−t==22 (2)(2)𝑡t==3𝑟3r
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)𝑟r==𝑡+5t+5 (2)(2)𝑟+3𝑡r+3t==−7−7
Identify if the following simultaneous equations are set up for the substitution method: (1)(1)3𝑏−4𝑎3b−4a==1414 (2)(2)5𝑏+5𝑎5b+5a==88
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.