Sure, let's solve the given system of equations using substitution. We have:
1. [tex]\( -4x + 3y = 3 \)[/tex]
2. [tex]\( y = 3x - 4 \)[/tex]
Here are the step-by-step instructions:
1. Substitute [tex]\( y \)[/tex] from the second equation into the first equation:
From the second equation, we already have: [tex]\( y = 3x - 4 \)[/tex]
Substitute this expression for [tex]\( y \)[/tex] into the first equation:
[tex]\[
-4x + 3(3x - 4) = 3
\][/tex]
2. Simplify the equation:
Distribute the 3 in the equation:
[tex]\[
-4x + 3 \cdot 3x - 3 \cdot 4 = 3
\][/tex]
[tex]\[
-4x + 9x - 12 = 3
\][/tex]
Combine like terms:
[tex]\[
5x - 12 = 3
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Add 12 to both sides of the equation:
[tex]\[
5x = 15
\][/tex]
Divide by 5:
[tex]\[
x = 3
\][/tex]
So, we have [tex]\( x = 3 \)[/tex].
4. Substitute [tex]\( x \)[/tex] back into the second equation to find [tex]\( y \)[/tex]:
Using [tex]\( y = 3x - 4 \)[/tex] and substituting [tex]\( x = 3 \)[/tex]:
[tex]\[
y = 3(3) - 4
\][/tex]
[tex]\[
y = 9 - 4
\][/tex]
[tex]\[
y = 5
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
x = 3 \\
y = 5
\][/tex]
This means the point [tex]\((3, 5)\)[/tex] satisfies both equations in the system.
