Solve the system of equations:
x + 2y = 3
4x + 5y = 6
multiply firat equation by 4
4 x + 8 y = 12
4 x + 5 y = 6
----------------subtract
3 y = 6
y = 2 etc
So x would equal 0?
no
x + 2 (2) = 3
x = -1
To solve the system of equations:
Step 1: Choose one of the equations and solve for one variable in terms of the other variable.
Let's choose the first equation and solve for x:
x + 2y = 3
Subtract 2y from both sides:
x = 3 - 2y
Step 2: Substitute this expression for x into the second equation.
4x + 5y = 6
Substituting x = 3 - 2y:
4(3 - 2y) + 5y = 6
Distribute 4 to both terms inside the parentheses:
12 - 8y + 5y = 6
Combine like terms:
-8y + 5y = 6 - 12
-3y = -6
Divide both sides by -3:
y = 2
Step 3: Substitute the value of y back into one of the original equations to solve for x.
Using the first equation:
x + 2(2) = 3
x + 4 = 3
Subtract 4 from both sides:
x = -1
So the solution to the system of equations is x = -1, y = 2.