If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation.
x + y = 2
3x + 2y = 9
To solve this system of equations using the substitution method, you first need to choose either equation to solve for one of the variables in terms of the other variable. Let's solve the first equation for x.
Given:
Equation 1: x + y = 2
Equation 2: 3x + 2y = 9
Solving Equation 1 for x:
x = 2 - y
Now, you substitute this expression for x into Equation 2:
3(2 - y) + 2y = 9
Simplifying this equation will determine the new equation after substituting the expression equivalent to x from the first equation into the second equation.
x + y = 2 Multiply both sides by 2
2 x + 2 y = 4
2 y = 4 - 2 x
3 x + 2 y = 9
3 x + 4 - 2 x = 9
x + 4 = 9
x = 9 - 4 = 5
x + y = 2
5 + y = 2
y = 2 - 5 = - 3