Question

GG.1 Is (x, y) a solution to the system of equations?
N46
Is (4,5) a solution to this system of equations?
y=
3
4
x+2
y=
5
4
x+4

Answer 1

To determine if \((4, 5)\) is a solution to the given system of equations, we need to substitute \(x = 4\) and \(y = 5\) into both equations and see if they hold true.

The given equations are:

1. \(y = \frac{3}{4}x + 2\)
2. \(y = \frac{5}{4}x + 4\)

Let's substitute \(x = 4\) into each equation:

**For the first equation:**

\[
y = \frac{3}{4}(4) + 2
\]
\[
y = 3 + 2
\]
\[
y = 5
\]

This means that \((4, 5)\) satisfies the first equation.

**For the second equation:**

\[
y = \frac{5}{4}(4) + 4
\]
\[
y = 5 + 4
\]
\[
y = 9
\]

This means that \((4, 5)\) does **not** satisfy the second equation.

Since \((4, 5)\) satisfies the first equation but not the second, \((4, 5)\) is **not a solution** to the system of equations.