Simultaneous Equations with Constants? What to doWatch
5𝑥 +4𝑘𝑦 = 6
3𝑥 −20𝑘𝑦 = 26
are simultaneous equations where k is a constant.
a) Show that 𝑥 = 2
b) Given that 𝑦 = −2, determine the value of 𝑘
I don't know what to do with the constant or what it represents
b) Use either eq and substitute your x value (you worked out for part a). Substitue y=-2. Solve to find k.
It is one of the basic steps for solving N Equations in N Unknowns.
In the present case, multiplying the first equation by 5 allows you to eliminate the ky term. The equations become
25 x + 20 ky = 30
3 x - 20 ky = 26
Now when these equations are added together, the result is
28 x = 56
Solving this equation for x is now simple.
Knowing x, and being given the value for y, either of the original equations can be used to plug these values in to solve for k.