I have been solving system of equations graphically and using addition and subtraction and now I'm being asked: Give any linear system of two equation that has a solution of (3,5). Does it have to be in y=mx+b form and if so how do I do it? I've been trying to find an example on net but all sites I've come across shows how to find the solution(order pairs) from system of equation and not how to write the equations when given only one ordered pair. Any help would be great thanks.
Hint:
Do you know how to find the equation of a straight line L1 passing through a given point (x0,y0)=(3,5) with a given slope m1 = 1.0 ?
Can you do the same for a line L2 with a slope m2=0.5?
Now solve the system of equations L1 and L2 and see what you get.
Try other values of m1 and m2 to generalize your findings.
To create a linear system of two equations with a solution of (3, 5), you do not necessarily need to express the equations in slope-intercept form (y = mx + b). However, using this form can often make it easier to create the equations.
To write the equations, you first need to determine the values of the slope (m) and y-intercept (b). With the given solution (3, 5), you can substitute these values into the slope-intercept form and solve for m and b.
Here's how you can do it:
Step 1: Plug in the given solution (3, 5) into the y = mx + b equation.
5 = 3m + b
Step 2: Choose any value for m. Let's say m = 2.
5 = 3(2) + b
Step 3: Solve for b.
5 = 6 + b
b = 5 - 6
b = -1
Step 4: Substitute the values of m and b back into the equation.
y = 2x - 1
So, the equation y = 2x - 1 is one possible equation that satisfies the given solution (3, 5).
However, note that there can be other valid equations too. For example, you can choose a different value for m (slope) and repeat the above steps to get another equation. It's also worth mentioning that you can write the equations in standard form (Ax + By = C) or other forms if required.