Sure! Let's solve the system of equations step-by-step:
We have the following two equations:
1. [tex]\( y = -x + 5 \)[/tex]
2. [tex]\( y = 2x - 1 \)[/tex]
Step 1: Set the two equations equal to each other since they both equal [tex]\( y \)[/tex]:
[tex]\[ -x + 5 = 2x - 1 \][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
First, add [tex]\( x \)[/tex] to both sides:
[tex]\[ 5 = 3x - 1 \][/tex]
Next, add 1 to both sides:
[tex]\[ 6 = 3x \][/tex]
Then, divide both sides by 3:
[tex]\[ x = 2 \][/tex]
Step 3: Substitute [tex]\( x = 2 \)[/tex] back into one of the original equations to find the value of [tex]\( y \)[/tex]. Let's use the second equation:
[tex]\[ y = 2x - 1 \][/tex]
[tex]\[ y = 2(2) - 1 \][/tex]
[tex]\[ y = 4 - 1 \][/tex]
[tex]\[ y = 3 \][/tex]
So, the solution to the system of equations is [tex]\( (x, y) = (2, 3) \)[/tex].
Enter the coordinates of the solution:
[tex]$\square$[/tex] 2
[tex]$\square$[/tex] 3
