Grade 9 – Chapter 6 – Lesson 2 Substitution

welcome back with new math list our lesson today about solving system of equation by substitution in this lesson we will know new method to solve the system of equation as we said before solving system of equations mean find the value of the variable which satisfy each equation so in this lesson we will know how to solve by using new method which is called substitution so question number one we need to use substitution to solve the system of equation equation number one equals two plus one and the three plus equals negative nine so the main point of solving we need one of the two equations has one variable at the left-hand side and all of the equation on the right-hand side you will find that in equation number one so we can say that's equation number one and that would be equation number two so we can say from one and two what are the meaning from one or two it's mean replace each for the second equation and replace it with the value of which is two plus one that is the meaning of substitution and rewrite the equation now so it would be 3x plus and instead of would replace it with 2x plus 1. thus we find it from the equation number one that's the equals to negative 9 now by solving the equation so 2x plus 3x equals 5x 5x plus 1 equals to negative 9. now by solving the equation we have positive 1 if you shift it will be negative 1. so we have 5x is equals to negative 10. now we can divide by five so we can say that is equal to negative two that is the value of so now we can using substitution at the equation number one so this will be equation number three now we can say from equation number three at equation number one what are the meaning from equation number three at equation number one as we said is equal to negative two so instead of will replace each with negative two so now we can rewrite the equation so is equals two multiplied by negative two plus one its mean is equal to negative four plus one equals to negative three so now we can say the solution will be negative two and negative three we have an order there it means must be written as and so the solution would be negative two and negative three in question number two we have equals four minus six and five plus three equals to negative one we need to solve the equation as we said before to solve the system of equation by substitution we need one equation that has one variable at the left-hand side and all of the equation at the right-hand side we will find that in equation number one so we can say that's equation number one and that's equation number two by the same way we can say from one or two it means replace each with four minus six now we can rewrite the equation so five plus three multiplied by four minus six all of that is equal to negative one now by solving the equation so we can write 5x plus by using distributive property so 3 times 4x equals 12x we multiplied by negative 6 equals to negative 80. all of that is equal to negative 1. now by solving the equation 5x and 12x equals 17x minus 18 is equal to negative 1 by solving the equation using the inverse operation so it would be by adding 18 so we have 17x is equals to positive 7 now we can divide by 17 then we can say that is equal to positive 1 and that is the value of and that would be equation number 3. as we're doing before so from equation number 3 at 1 what are the meaning from equation number three at one it's mean from the equation number one replace each with one so it will be equals four multiplied by one minus six now we have is equal four minus six equals to negative two and that's the value of so we can say the solution would be the ordered pair 1 and negative 2. it's mean if you replace with 1 and replace with negative 2 you will find that the left-hand side is equal to the right-hand side in question number 3 we need to solve plus 2y equals 6 and the 3x minus 4y equals 20 by using substitution as we said before to solve the equation by using substitution we need one equation that has variable in the left-hand side and all of the equation at the right-hand side so if you look at the equation number one and the equation number two you will not find in one of them so we need one variable at the left and all of the variables right which one that we'll choose we'll shoot the variable that has coefficient equals one so we'll find that is equals 1. so we can shift 2y to the other side 2y is positive so it would be negative 2y so we can say equation number 1 is equals 6 minus 2y and that would be defined by the equation above that's would be equation number two by the same way we can say from equation number one add equation number two what are the meaning from equation number one at equation number two by the same way and instead of replaced with six minus two so instead of will replace it with 6 minus 2y then rewrite the equation number 2. so it will be equals 3 multiplied by 6 minus 2y minus 4y equals 28. so by using distributive property so 3 times 6 equals 80 minus 3 times 2 equals 6y minus 4y equals 28. now by solving the equation because this 18 is positive we can shift it to by subtracting it negative 6y minus 4y equals negative 10y equals 28 minus 18 equals positive 10. now you can divide by negative 10. so we can say that is equals 10 divided by negative 10 equals to negative one and that is the value of now from equation number three at equation number one it's mean replace each with negative one so instead of i'll replace it with negative one that's mean is equal six minus two multiplied by negative one then is equals six minus two times negative one it would be negative two minus negative two it will be plus two it's mean is equals to eight now we find the value of and the value of so we can say the solution would be don't say negative one and we said the ordered pair we have to start from to so the solution now will be eight and negative one that's how we can solve by using substitution in question number four we have 4x plus 5y equals 11 minus 3x equals negative 30. we need to solve this system of equation by using substitution we said to solve by using substitution we need one variable at the left hand side and all of the variable at the right hand side you will not find at the equation number one and the equation number two if you didn't find we need to find the variable that has coefficient equals one so we'll find that we have equals one so we'll use this equation now we have shifting 3x to the other side it was negative 3x so it would be by adding 3x so the equation now would be equals 3x minus 30. and that's will be equation number one and the second equation now would be equation number two we can say from equation number one at from equation number one at equation number two it's mean replacing each with three minus thirty now rewrite the equation so it would be 4x plus 5y 5 and instead of wire blessed with 3x minus 30. all of that is equal to positive now we can solve the equation that's 4x plus 5 times 3 equals 15x minus 5 times 13 equals 65 all of that is equal to 11. now 4x plus 15x equals 19x minus 65 is equal to 11. by solving the equation that's negative it will be positive 65. so we have 19x as equals 76. now dividing by 19 that's mean is equal to 4. after finding the value of that would be equation number three from equation number three at equation number one from equation number three equation number one it means replace with four so now rewrite the equation equals three multiply multiplied by 4 minus 30. that's mean equals 3 times 4 equals 1 minus 13 equals negative 1 and that is the value of so we can say that the solution will be 4 and negative 1. you have to start with then end with