Question

Mindy wants to solve the following system using the elimination method:

y = x − 4
y = 2x − 3

What number should the equation y = x − 4 be multiplied by to eliminate x?

Answer 1

y = x – 4 y = 2x – 3 We want to eliminate x, so we need to multiply the first equation by a number that will make the x term equal to the x term in the second equation. In other words, we need to find a number that will make the coefficient of x in the first equation equal to the coefficient of x in the second equation. The coefficient of x in the first equation is 1, and the coefficient of x in the second equation is 2. To make these coefficients equal, we need to multiply the first equation by 2. So, we get: 2y = 2x – 8 Now we can use this equation to eliminate x: 2y = 2x – 8 y = 2x – 3 Subtracting the second equation from the first, we get: 0 = -5 This is a contradiction, which means that the system has no solution.
Therefore, the answer to the question is: 2. Note: If the system had a solution, we would continue with the elimination method to find the values of x and y. But since the system has no solution, we stop here. I hope this helps! Let me know if you have any questions. Best, Jen

Answer 2

To use the elimination method to solve this system of equations, we want to eliminate one of the variables (either x or y) by adding or subtracting the two equations. In this case, we can eliminate x by adding the two equations together.

When we add the two equations, we get:

y + y = x - 4 + 2x - 3

Simplifying this equation, we get:

2y = 3x - 7

Now we can see that we have an equation with both x and y, and we can use this to solve for one of the variables in terms of the other. To eliminate x, we need to rearrange this equation so that it is in the form y = mx + b:

3x = 2y + 7

x = (2/3)y + 7/3

Now we can see that the equation y = x - 4 needs to be multiplied by 2 in order to eliminate x:

2(y = x - 4) becomes 2y = 2x - 8

We can substitute the expression we found for x above into this equation to get:

2y = 2((2/3)y + 7/3) - 8

Simplifying this equation, we get:

2y = (4/3)y + 10/3

Now we can solve for y:

(2/3)y = 10/3

y = 5

Substituting y = 5 back into one of the original equations, we can solve for x:

y = x - 4

5 = x - 4

x = 9

Therefore, the solution to the system of equations is (x,y) = (9,5).