Question

A system of equations is shown: 4x = −3y 17 3x − 4y = −6 what is the solution to this system of equations?

a) (−2, −3)
b) (3, 2)
c) (2, 3)
d) (−3, −2)

Answer 1

To find the solution to this system of equations, we can use the method of substitution or elimination. Using the method of substitution, the solution to the system of equations is (2, 3).

Step-by-step explanation:

To find the solution to this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

Step 1: Solve one equation for one variable. We can solve the first equation for x: 4x = -3y + 17 ⇒ x = (-3y + 17)/4

Step 2: Substitute the expression for x into the other equation. The second equation becomes: 3((-3y + 17)/4) - 4y = -6

Step 3: Solve for y. Simplify the equation and solve for y: -9y + 51 - 16y = -24 ⇒ -25y = -75 ⇒ y = 3

Step 4: Substitute the value of y back into the equation for x. Use the first equation: 4x = -3(3) + 17 ⇒ 4x = -9 + 17 ⇒ 4x = 8 ⇒ x = 2

Therefore, the solution to the system of equations is (2, 3).