Question

Use the system of equations to answer the question.
2x + 3y = 8
x-y=5

Answer 1

To solve the system of equations, find the values of x and y that satisfy both equations simultaneously. After isolating y from x - y = 5 and substituting into 2x + 3y = 8, we get y = -2/5 and x = 23/5 as the solution.

Step-by-step explanation:

To solve the system of equations:
2x + 3y = 8
x - y = 5
we need to find the values of x and y that satisfy both equations.

Step 1: Solve the second equation for x.

x = y + 5

Step 2: Substitute the expression for x into the first equation.

2(y + 5) + 3y = 8

Step 3: Simplify and solve for y.

2y + 10 + 3y = 8
5y + 10 = 8
5y = -2
y = -2/5

Step 4: Substitute the value of y back into the equation from Step 1 to solve for x.

x = (-2/5) + 5
x = (23/5)

Therefore, the solution to the system of equations is x = 23/5 and y = -2/5.

Answer 2

x = 23/5

y = -2/5

Step-by-step explanation:

We are given two equations

2x + 3y = 8 eq. 1

x - y = 5 eq. 2

From eq. 2

x - y = 5

x = 5 + y eq. 3

Substitute eq. 3 into eq. 1

2x + 3y = 8 eq. 1

2(5 + y) + 3y = 8

Simplify the equation

10 + 2y + 3y = 8

10 + 5y = 8

5y = 8 - 10

5y = -2

y = -2/5

or

y = -0.4

Substitute the value of y into eq. 3 to get the value of x

x = 5 + y eq. 3

x = 5 - 2/5

x = 23/5

or

x = 4.6

Therefore, the solution set is

(x, y) = (23/5, -2/5)

This is the point of intersection where these two equations meet.