What is the solution of the system of equations?
13x−6y=2
3x−4y=−10
Enter your answer in the boxes.
try writing them as
26x - 12y = 4
9x - 12y = -30
Now just subtract the equations and the y's will vanish.
So the answer would be 15, -3?
To find the solution of the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:
13x - 6y = 2
13x = 2 + 6y
x = (2 + 6y) / 13
2. Substitute the expression we found for x into the other equation:
3x - 4y = -10
3((2 + 6y) / 13) - 4y = -10
Multiply both sides by 13 to eliminate the denominator:
6 + 18y - 52y = -130
-34y = -136
Divide both sides by -34:
y = 4
3. Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
13x - 6y = 2
13x - 6(4) = 2
13x - 24 = 2
13x = 26
x = 2
Therefore, the solution of the system of equations is x = 2 and y = 4.