Question

4x + 3y = 18
4x - 2y = 18

Answer 1

(4.5,0)

Explanation:

The point that makes this system of equations true is (4.5,0.

When x=4.5, and y=0 both of these equations equal each other.

You can find this point either by using your calculator, or graphing the equations and seeing where they intersect.

Answer 2

To solve the system of linear equations:

4x + 3y = 18

4x - 2y = 18

we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the equations in a way that eliminates one of the variables. Here's how we can do it:

Multiply the first equation by 2, and the second equation by 3 to eliminate x:

8x + 6y = 36

12x - 6y = 54

Now, subtract the second equation from the first:

8x + 6y - (12x - 6y) = 36 - 54

8x + 6y - 12x + 6y = -18

-4x + 12y = -18

Divide both sides by -4 to isolate x:

-4x/(-4) + 12y/(-4) = -18/(-4)

x - 3y = 4.5

Now, we can substitute this value of x into one of the original equations, let's use the first equation:

4(4.5) + 3y = 18

18 + 3y = 18

3y = 18 - 18

3y = 0

y = 0

So, the solution to the system of equations is x = 4.5 and y = 0.

Method 2: Substitution

In this method, we solve one of the equations for one variable and then substitute that expression into the other equation to solve for the other variable. Here's how we can do it:

Solve the first equation for x:

4x + 3y = 18

4x = 18 - 3y

x = (18 - 3y)/4

Now, substitute this expression for x into the second equation:

4[(18 - 3y)/4] - 2y = 18

18 - 3y - 2y = 18

-5y = 18 - 18

-5y = 0

y = 0

Now, substitute this value of y back into the expression for x:

x = (18 - 3(0))/4

x = 18/4

x = 4.5

So, the solution to the system of equations is x = 4.5 and y = 0, which is consistent with the solution obtained using the elimination method.