2. What is the value of x in the solution to the system of equations below?
15x – 12y = 13
30x + 9y = 4
multiply the 1st by 3 : 45x - 36y = 39
multiply the 2nd by 4: 120x + 36y = 16
add them:
165x = 55
x = 55/165 = 1/3
sub back into the 2nd
30(1/3) + 9y = 4
10 + 9y = 4
9y = -6
y = -2/3
To find the value of x in the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to solve this system.
Step 1: Multiply the first equation by 2.
2(15x – 12y) = 2(13)
30x – 24y = 26
Step 2: Subtract the second equation from the equation obtained in Step 1.
(30x – 24y) - (30x + 9y) = 26 - 4
30x - 30x - 24y - 9y = 22
-33y = 22
Step 3: Solve for y.
To isolate y, we divide both sides of the equation by -33.
-33y / -33 = 22 / -33
y = -22/33
y = -2/3
Step 4: Substitute the value of y into either of the original equations to solve for x.
Let's substitute y = -2/3 into the first equation:
15x - 12(-2/3) = 13
15x + 8 = 13
15x = 13 - 8
15x = 5
x = 5/15
x = 1/3
Therefore, the value of x in the solution to the system of equations is x = 1/3.