Question

Solve the following system of equations using the substitution method.
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5x+3y=1 and x+2y=3

Answer 1

To solve this system using the substitution method, we need to isolate one variable in one equation and substitute it into the other equation. Here's how to do it:

1. Solve one of the equations for x or y. Let's solve the second equation for x:
x + 2y = 3
x = 3 - 2y

2. Substitute the expression you just found for x into the other equation:
5x + 3y = 1
5(3 - 2y) + 3y = 1

3. Simplify and solve for y:
15 - 10y + 3y = 1
-7y = -14
y = 2

4. Substitute y = 2 into one of the original equations to find x:
x + 2y = 3
x + 2(2) = 3
x = -1

So the solution to the system is (x, y) = (-1, 2).