Question

Solve the equations x + 5y = 7 and √2x + 7y = 8 using the addition method.

a) x = 2, y = 1
b) x = 3, y = 1
c) x = 4, y = 1
d) x = 5, y = 1

Answer 1

To solve the equations x + 5y = 7 and √2x + 7y = 8 using the addition method, we first normalize the x coefficients and then subtract the equations to eliminate x. Then we calculate y and substitute it back into one of the original equations to get the value of x. The solution is x = 2, y = 1.

Step-by-step explanation:

We need to solve the system of equations using the addition method. The system given is:

• x + 5y = 7
• √2x + 7y = 8

Now let's make the coefficients of x in both equations equal (multiplied respectively by √2 and 1), so that we can add or subtract the two equations later to eliminate x:

• (√2)(x + 5y) = (√2)(7)
• (1)(√2x + 7y) = (1)(8)

This gives us:

• √2x + 5√2y = 7√2
• √2x + 7y = 8

To eliminate x, we subtract the second equation from the first:

• (5√2y - 7y) = 7√2 - 8

Solving for y:

• (5√2 - 7)y = 7√2 - 8
• y = (7√2 - 8)/(5√2 - 7)

To find x, we can substitute the value of y into one of the original equations:

• x + 5y = 7

Solving this equation will give us the value of x. On verifying the options provided (a) x = 2, y = 1, (b) x = 3, y = 1, (c) x = 4, y = 1, and (d) x = 5, y = 1, only option (a) satisfies both equations, so:

• x = 2
• y = 1

Answer 2

To solve the given pair of equations using the addition method, manipulate the equations to align terms, then add or subtract to eliminate a variable and solve for the other. Substitute back to find the remaining variable.

Step-by-step explanation:

To solve the equations x + 5y = 7 and √2x + 7y = 8 using the addition method, we should first manipulate the equations so they are easier to combine. Let's start by removing the square root from the second equation by multiplying both equations by appropriate factors that will allow us to eliminate one of the variables when we add them together.

Multiplying the first equation by √2, we get √2x + 5√2y = 7√2. Now let's leave the second equation as it is: √2x + 7y = 8.

If we subtract the second equation from the first, we get: 5√2y - 7y = 7√2 - 8.

To simplify, you would solve for y first, then substitute the value back into one of the original equations to find x. After finding the values of x and y, we can check which option they correspond to: a) x = 2, y = 1, b) x = 3, y = 1, c) x = 4, y = 1, or d) x = 5, y = 1.