Jasmine decides to solve this system of equations using the substitution method
3x + y = 18
4x + 2y = 10
which equation should be solved in step 3 using jasmines method
In the substitution method, we solve one equation for a variable and then substitute that expression into the other equation. This allows us to solve for the other variable.
In this case, we can solve the first equation for y:
3x + y = 18
y = 18 - 3x
Now, we substitute this expression for y in the second equation:
4x + 2(18 - 3x) = 10
Simplifying this equation, we get:
4x + 36 - 6x = 10
This is the equation that Jasmine should solve in step 3 using the substitution method.
In step 3 of the substitution method, Jasmine should solve one of the equations for one variable and substitute it into the other equation.
To determine which equation should be solved in step 3, we need to look for an equation where one variable is already isolated.
Let's check the equations:
Equation 1: 3x + y = 18
Equation 2: 4x + 2y = 10
In equation 1, neither variable is isolated since there are coefficients in front of both x and y.
In equation 2, both variables have coefficients in front of them, making it harder to isolate one of them.
Since none of the equations have a variable already isolated, Jasmine can choose any equation to solve for one variable.
So, the equation Jasmine can solve in step 3 using the substitution method can be either Equation 1 (3x + y = 18) or Equation 2 (4x + 2y = 10).
To solve the system of equations using the substitution method, Jasmine needs to solve one of the equations for one variable and then substitute that expression into the other equation. This will form a new equation with just one variable, which she can solve to find the value of that variable. Once she has found the value of one variable, she can substitute it back into one of the original equations to find the value of the other variable.
In this case, let's go through the steps with the given system of equations:
Step 1: Write down the two equations.
3x + y = 18
4x + 2y = 10
Step 2: Choose one equation to solve for one variable. Let's solve the first equation for y.
3x + y = 18
Subtract 3x from both sides:
y = 18 - 3x
Step 3: Substitute the expression for y into the other equation.
4x + 2y = 10
Substitute y = 18 - 3x:
4x + 2(18 - 3x) = 10
So, the equation that should be solved in Step 3 using Jasmine's method is: 4x + 2(18 - 3x) = 10.