Question

What statement is true of the system of equations? 4x − 5y = 4 2x+3y = 2

a. the solution is (0, 1).
b. the solution is (1, 0).
c. the system has no solution.
d. the system has infinitely many solutions.

Answer 1

To solve the system of equations, use the substitution method to find the values of x and y.

Step-by-step explanation:

To determine the solution to the given system of equations, we can use a method called substitution. First, let's solve the second equation for x: 2x + 3y = 2. Subtract 3y from both sides to isolate x, giving us 2x = 2 - 3y. Divide both sides by 2 to solve for x, yielding x = (2 - 3y) / 2. Now substitute this expression for x in the first equation: 4((2 - 3y) / 2) - 5y = 4. Simplify this equation to find the value of y. Finally, substitute the value of y back into the second equation to find the value of x.