Question

How to solve by substitution

Answer 1

Yes, you can solve a system of linear equations by substitution. In the context of the provided graph and equations, the point of intersection (4, 5) indicates the solution to the system of equations y = x + 1 and
`y = 6 - (1)/(4)x` .

Yes, you can solve a system of linear equations by substitution. In the context of the provided graph and equations, the point of intersection (4, 5) indicates the solution to the system of equations y = x + 1 and
`y = 6 - (1)/(4)x` .

To solve the system by substitution, you would set the expressions for
`\(y\)` equal to each other:

`\[ x + 1 = 6 - (1)/(4)x \]`

Then, you would solve for
`\(x\)`:

`\[ x + (1)/(4)x = 6 - 1 \]`

Combine like terms:

`\[ (5)/(4)x = 5 \]`

Solve for
`\(x\)`:

`\[ x = 4 \]`

Now that you have the value of
`\(x\)`, substitute it back into one of the original equations to find
`\(y\)`. Using the first equation
`\(y = x + 1\)`:

`\[ y = 4 + 1 = 5 \]`

So, the solution to the system of equations is
`\(x = 4\) and \(y = 5\)`, which matches the given point of intersection (4, 5) on the graph. This confirms that the point (4, 5) is a valid solution to the system of equations.