4x+6y=21
7x-3y=3
multiply the 2nd equation by 2 , and add the result to the 1st equation
...this will eliminate the x-term
solve the resulting equation for y
... substitute back to find x
actually, if you follow step 1, you eliminate y. But then just use the x value obtained to find y.
To find the solution to this system of equations, we will use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
4x + 6y = 21
Subtract 6y from both sides:
4x = 21 - 6y
Divide both sides by 4:
x = (21 - 6y) / 4
Step 2: Substitute the expression we found for x into the second equation.
7x - 3y = 3
Substitute x with (21 - 6y) / 4:
7((21 - 6y) / 4) - 3y = 3
Now we can solve for y.
Step 3: Simplify and solve the equation for y.
Multiply both sides by 4 to eliminate the fraction:
7(21 - 6y) - 12y = 12
147 - 42y - 12y = 12
Combine like terms:
-54y = -135
Divide both sides by -54:
y = (-135) / (-54)
y = 5/2 or 2.5
Step 4: Substitute the value of y into the expression we found for x to find x.
x = (21 - 6(2.5)) / 4
x = (21 - 15) / 4
x = 6 / 4
x = 3/2 or 1.5
So the solution to the system of equations is x = 1.5 and y = 2.5.