Question

Find a solution to the following system of equations.
−5x + 2y = 9
3x + 5y = 7


(–1, 2)


(0, 1)


(–9, 7)


(1, 7)

Answer 1

To find the solution to the system of equations, we can solve it using either the substitution method or the elimination method. Let's use the elimination method.

First, we'll multiply the first equation by 3 and the second equation by -5 to get the same coefficient for x:

-5x + 2y = 9 (multiply by 3)
3x + 5y = 7 (multiply by -5)

This gives us:

-15x + 6y = 27
-15x - 25y = -35

Next, we'll subtract the equations to eliminate x:

(-15x + 6y) - (-15x - 25y) = 27 - (-35)
This simplifies to:
-15x + 6y + 15x + 25y = 27 + 35

Combining like terms, we have:
31y = 62

Dividing both sides of the equation by 31, we find:
y = 2

Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-5x + 2y = 9

Substituting y=2, we have:
-5x + 2(2) = 9
-5x + 4 = 9

Subtracting 4 from both sides, we have:
-5x = 5

Dividing both sides by -5, we find:
x = -1

Therefore, the solution to the system of equations is (-1, 2).

The correct answer is (–1, 2).