what is the solution of the system of equations? y=4x+1 y=5x-9
i believe x = 10, just set the equations equal to one another
how exactly would you do that though? im completely lost :(
solving 2 equations means you want the y of one equation to be equal to y of the other, and the same for the x's
so
y = y
5x-9 = 4x+1
5x - 4x = +1 + 9
x = 10
sub that back into either of the originals
y = 4x+1
y = 4(10) + 1
y = 41
notice you would have gotten the same y had you subbed into the second
so x = 10, y = 41
To find the solution of a system of equations, you need to solve the equations simultaneously. In this case, you have two equations: y = 4x + 1 and y = 5x - 9.
To solve the system, you can use the method of substitution or elimination. Let's use the substitution method:
Step 1: Start with one of the equations and solve it for one variable in terms of the other. Let's solve the first equation, y = 4x + 1, for y in terms of x:
y = 4x + 1
Step 2: Substitute this expression for y in the second equation, y = 5x - 9:
4x + 1 = 5x - 9
Step 3: Simplify the equation by moving all the terms involving x to one side:
4x - 5x = -9 - 1
-x = -10
Step 4: Divide both sides of the equation by -1 to solve for x:
x = -10 / -1
x = 10
Step 5: Now that you have the value of x, substitute it back into one of the original equations to find the value of y. Using the first equation, y = 4x + 1:
y = 4(10) + 1
y = 40 + 1
y = 41
Therefore, the solution to the system of equations y = 4x + 1 and y = 5x - 9 is x = 10 and y = 41.