Question

Use substitution to solve the system
5x+2y=15
-2x+y=3

Answer 1

To solve the system using substitution, we need to solve one of the equations for one of the variables, and then substitute the expression into the other equation.

Let's solve the second equation for y:
-2x + y = 3
y = 2x + 3

Now we can substitute this expression for y into the first equation:
5x + 2y = 15
5x + 2(2x + 3) = 15

Simplifying the equation, we get:
5x + 4x + 6 = 15
9x = 9
x = 1

Now that we know x = 1, we can substitute this value back into the equation we found for y:
y = 2x + 3
y = 2(1) + 3
y = 5

Therefore, the solution to the system of equations is x = 1 and y = 5.

Answer 2

x = 1, y = 5

Explanation:

- 2x + y = 3

Add 2x on both sides

y = 3 + 2x

5x + 2y = 15

5x + 2(3 + 2x) = 15

5x + 2(3) + 2(2x) = 15

5x + 6 + 4x = 15

5x + 4x = 15 - 6

9x = 9

x = 9/9

x = 1

y = 3 + 2x

= 3 + 2(1)

= 3 + 2

y = 5