Solve the linear system graphically
(Dont graph it just solve it)
x+ 2y = 8
3x+ 4y = 20
double the first:
2x + 4y = 16
subtract from the 2nd
x = 4
back into the 1st:
4 + 2y = 8
2y = 4
y = 2
x = 4, y = 2
To solve a linear system graphically, we would typically plot the equations on a graph and find the point of intersection. However, since you specifically requested a non-graphical solution, we can solve the system algebraically using the method of substitution.
Step 1: Solve one of the equations for one variable.
Let's solve the first equation for x:
x = 8 - 2y [Equation 1]
Step 2: Substitute the expression for x in the second equation.
Substituting the value of x from Equation 1 into the second equation, we have:
3(8 - 2y) + 4y = 20
Step 3: Simplify and solve for y.
Expanding and simplifying the equation, we get:
24 - 6y + 4y = 20
Combine like terms:
-2y + 24 = 20
Subtract 24 from both sides:
-2y = 20 - 24
-2y = -4
Divide both sides by -2:
y = -4 / -2
y = 2
Step 4: Substitute the value of y into the first equation to find x.
Using Equation 1, substitute y = 2:
x = 8 - 2(2)
x = 8 - 4
x = 4
Therefore, the solution to the linear system is x = 4 and y = 2.