Question
Explain step by step how to solve 3x + y = 2
And 7x-4y=30 to end up with (2, -4)
And 7x-4y=30 to end up with (2, -4)
Answers
GPT 3.5
First, we can solve the system of equations 3x + y = 2 and 7x - 4y = 30.
Step 1: Start with the equation 3x + y = 2.
This equation can be rewritten as y = -3x + 2.
Step 2: Substitute the expression for y into the second equation 7x - 4(-3x + 2) = 30.
Simplify the equation: 7x + 12x - 8 = 30.
Combine like terms: 19x - 8 = 30.
Add 8 to both sides: 19x = 38.
Divide by 19: x = 2.
Step 3: Substitute the value of x back into the equation y = -3x + 2.
y = -3(2) + 2.
y = -6 + 2.
y = -4.
Therefore, the solution to the system of equations 3x + y = 2 and 7x - 4y = 30 is x = 2 and y = -4, giving the point of intersection as (2, -4).
Step 1: Start with the equation 3x + y = 2.
This equation can be rewritten as y = -3x + 2.
Step 2: Substitute the expression for y into the second equation 7x - 4(-3x + 2) = 30.
Simplify the equation: 7x + 12x - 8 = 30.
Combine like terms: 19x - 8 = 30.
Add 8 to both sides: 19x = 38.
Divide by 19: x = 2.
Step 3: Substitute the value of x back into the equation y = -3x + 2.
y = -3(2) + 2.
y = -6 + 2.
y = -4.
Therefore, the solution to the system of equations 3x + y = 2 and 7x - 4y = 30 is x = 2 and y = -4, giving the point of intersection as (2, -4).