Q:

# PLEASE ANSWER ASAP!!! SHOW ALL THE STEPS.Solve the system of equations using elimination. Make sure to show all work and find the value of both x and y 1. x - 3y = 73x + 3y = 92. 8x+ 3y = 14x + 2y = 0

Accepted Solution

A:
Answer:For the first question $$x = 4\\ y = -1$$ and For the second question $$x = 0.5\\ y = -1$$ Step-by-step explanation:Given:1.x - 3y = 73x + 3y = 92.8x+ 3y = 14x + 2y = 0Elimination method :In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get$$(x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = \frac{16}{4}\\x = 4$$Now substitute X equal to 4 in equation x -3y = 7 we get$$4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = \frac{3}{-3}\\ y = -1\\$$This way we have x is equal to 4 and y is equal to -1  for question number 1. For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get$$8x + 4y = 0\\$$Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get$$(8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1$$Now substitute y equal to -1 in equation 8x +3y = 1 we get$$8x + 3\times -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = \frac{4}{8}\\ x = 0.5\\$$This way we have x is equal to 0.5 and y is equal to -1  for question number 2.