Question

Can you find the solution of a system of linear equations with the same y-intercept but different slopes without graphing? Explain.

a) Yes, by using the method of substitution.
b) No, because different slopes will always result in different y-intercepts.
c) Yes, by using the method of elimination.
d) No, because it's impossible for two lines with different slopes to have the same y-intercept.

Answer 1

Yes, by using the method of elimination.

Step-by-step explanation:

When two lines have the same y-intercept but different slopes, it is possible to find the solution of the system of linear equations without graphing. This can be done using the method of elimination. The key idea is to eliminate one variable by adding or subtracting the equations to create a new equation with only one variable, then solve for that variable. Once you have the value of one variable, you can substitute it into one of the original equations to find the value of the other variable.