Use substitution to solve the system.

[tex]\[
\begin{aligned}
5x + 4y &= 7 \\
y &= 2x + 5
\end{aligned}
\][/tex]

[tex]\[
\begin{array}{l}
x = \\
y =
\end{array}
\][/tex]

[tex]\[\square \quad \square\][/tex]



Answer :

Let's solve the system of equations using the substitution method. The system of equations is:

[tex]\[ \begin{aligned} 5x + 4y &= 7 \quad \text{(Equation 1)} \\ y &= 2x + 5 \quad \text{(Equation 2)} \end{aligned} \][/tex]

Step 1: Substitute Equation 2 into Equation 1

From Equation 2, we have:
[tex]\[ y = 2x + 5 \][/tex]

We can substitute this expression for \( y \) into Equation 1:

[tex]\[ 5x + 4(2x + 5) = 7 \][/tex]

Step 2: Simplify and solve for \( x \)

Distribute the \( 4 \) inside the parentheses:

[tex]\[ 5x + 8x + 20 = 7 \][/tex]

Combine the \( x \) terms:

[tex]\[ 13x + 20 = 7 \][/tex]

Subtract 20 from both sides to isolate the \( x \) term:

[tex]\[ 13x = 7 - 20 \][/tex]

Simplify the right side:

[tex]\[ 13x = -13 \][/tex]

Divide both sides by 13:

[tex]\[ x = \frac{-13}{13} \][/tex]

So,

[tex]\[ x = -1 \][/tex]

Step 3: Substitute \( x = -1 \) back into Equation 2 to solve for \( y \)

We use Equation 2 to find the corresponding \( y \) value:

[tex]\[ y = 2(-1) + 5 \][/tex]

Simplify:

[tex]\[ y = -2 + 5 \][/tex]

Therefore,

[tex]\[ y = 3 \][/tex]

Solution

The solution to the system of equations is:

[tex]\[ \begin{array}{l} x = -1 \\ y = 3 \end{array} \][/tex]

So, the point [tex]\((x, y) = (-1, 3)\)[/tex] satisfies both equations in the given system.