Solve the system of equations using substitution.
y = 2x + 3
y = 3x + 1
2x + 3 = 3x + 1
2 = x
y = 7
To solve the system of equations using substitution, we need to express one of the variables in terms of the other variable and substitute it into the other equation. Let's solve this step by step:
Step 1: Express y in terms of x in the first equation.
Given equation 1: y = 2x + 3
Step 2: Substitute the expression for y in equation 1 into equation 2.
Given equation 2: y = 3x + 1
Substitute the expression for y from equation 1:
2x + 3 = 3x + 1
Step 3: Simplify the equation by combining like terms.
Subtract 2x from both sides of the equation:
2x + 3 - 2x = 3x + 1 - 2x
Simplify:
3 = x + 1
Step 4: Solve for x.
Subtract 1 from both sides of the equation:
3 - 1 = x + 1 - 1
2 = x
Step 5: Substitute the value of x back into either equation to solve for y.
Let's use equation 1:
y = 2x + 3
Substituting x = 2:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the solution to the system of equations is x = 2 and y = 7.