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A system of equations is graphed on the coordinate plane.
[tex]\[
\begin{array}{l}
y = -x + 5 \\
y = 2x - 1
\end{array}
\][/tex]

What is the solution to the system of equations?
Enter the coordinates of the solution in the boxes.
[tex]\[
\square \quad \square
\][/tex]

Sagot :

GinnyAnsweridn
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
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