Crossing Lines Practice Worksheet
Algebra 1 • Systems of Equations
CROSSING LINES
Solving Linear Systems by Graphing on a Coordinate Plane
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PART 1: SLOPE-INTERCEPT FORM — Graph both lines using their slope (\(m\)) and \(y\)-intercept (\(b\)). Identify and state the point of intersection \((x, y)\).
Problem 1 Both in \(y = mx + b\)
\(\begin{cases} y = 2x - 1 \\ y = -x + 5 \end{cases}\)
Line 1: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Line 2: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Check: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Problem 2 Both in \(y = mx + b\)
\(\begin{cases} y = -\frac{1}{2}x + 3 \\ y = x - 3 \end{cases}\)
Line 1: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Line 2: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Check: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Problem 3 Both in \(y = mx + b\)
\(\begin{cases} y = \frac{2}{3}x - 2 \\ y = -x + 3 \end{cases}\)
Line 1: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Line 2: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Check: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Problem 4 Both in \(y = mx + b\)
\(\begin{cases} y = -2x - 4 \\ y = \frac{1}{2}x + 1 \end{cases}\)
Line 1: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Line 2: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Check: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Crossing Lines • Graphing Practice Worksheet Page 1 of 3
Crossing Lines • Linear Systems Class Practice • Page 2 of 3
Problem 5 Both in \(y = mx + b\)
\(\begin{cases} y = \frac{3}{4}x - 1 \\ y = -\frac{1}{2}x + 4 \end{cases}\)
Line 1: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Line 2: \(m = \underline{\hspace{24px}}\), \(b = \underline{\hspace{24px}}\)
Show work / check values:
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Verify: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Strategy Tip PART 2: MIXED FORMS (STANDARD & SLOPE-INTERCEPT)
One equation is written in Standard Form (\(Ax + By = C\)). First isolate \(y\) to write it in slope-intercept form (\(y = mx + b\)), or calculate the \(x\)-intercept (set \(y=0\)) and \(y\)-intercept (set \(x=0\)) to plot the line.
Problem 6 Standard + Slope-Int
\(\begin{cases} 2x + y = 4 \\ y = x - 2 \end{cases}\)
Rewrite \(2x + y = 4 \implies y = \underline{\hspace{40px}}\)
Line 2: \(m = \underline{\hspace{20px}}\), \(b = \underline{\hspace{20px}}\)
Work space / Intercepts:
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Verify: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Problem 7 Standard + Slope-Int
\(\begin{cases} x - 2y = 6 \\ y = -2x + 2 \end{cases}\)
Rewrite \(x - 2y = 6 \implies y = \underline{\hspace{40px}}\)
Line 2: \(m = \underline{\hspace{20px}}\), \(b = \underline{\hspace{20px}}\)
Work space / Intercepts:
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Verify: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Crossing Lines • Graphing Practice Worksheet Page 2 of 3
Crossing Lines • Linear Systems Class Practice • Page 3 of 3
Problem 8 Standard + Slope-Int
\(\begin{cases} 3x + 4y = 12 \\ y = \frac{3}{2}x - 6 \end{cases}\)
Rewrite \(3x + 4y = 12 \implies y = \underline{\hspace{40px}}\)
Line 2: \(m = \underline{\hspace{20px}}\), \(b = \underline{\hspace{20px}}\)
Work space / Intercepts:
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Verify: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Problem 9 Standard + Slope-Int
\(\begin{cases} x + y = -3 \\ y = 3x + 5 \end{cases}\)
Rewrite \(x + y = -3 \implies y = \underline{\hspace{40px}}\)
Line 2: \(m = \underline{\hspace{20px}}\), \(b = \underline{\hspace{20px}}\)
Work space / Intercepts:
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Verify: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Problem 10 Standard + Slope-Int
\(\begin{cases} 2x - 3y = 12 \\ y = -x + 1 \end{cases}\)
Rewrite \(2x - 3y = 12 \implies y = \underline{\hspace{40px}}\)
Line 2: \(m = \underline{\hspace{20px}}\), \(b = \underline{\hspace{20px}}\)
Work space / Intercepts:
Solution:
\((x, y) = (\underline{\hspace{32px}}, \underline{\hspace{32px}})\)
Verify: (____, ____)
x y -10 -5 5 10 10 5 -5 -10
Solution Summary Log Record your final coordinate pairs \((x, y)\) below for quick checking.
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
Crossing Lines • Graphing Practice Worksheet Page 3 of 3
Crossing Lines Answer Key
Teacher Edition Complete Solutions & Graphs
CROSSING LINES — ANSWER KEY
Solving Linear Systems by Graphing • Problems 1 to 4
Grid: [-10, 10]
All integer solutions
Line 1 Line 2 Point of Intersection \((x, y)\)
Problem 1 Solution: \((2, 3)\)
\(\begin{cases} \color{#2563eb}{y = 2x - 1} \\ \color{#dc2626}{y = -x + 5} \end{cases}\)
Line 1: \(m = 2 = \frac{2}{1}\), \(b = -1\)
Line 2: \(m = -1 = \frac{-1}{1}\), \(b = 5\)
Check \((2, 3)\): \(3 = 2(2) - 1 = 3\) ✓ | \(3 = -(2) + 5 = 3\) ✓
Problem 2 Solution: \((4, 1)\)
\(\begin{cases} \color{#2563eb}{y = -\frac{1}{2}x + 3} \\ \color{#dc2626}{y = x - 3} \end{cases}\)
Line 1: \(m = -\frac{1}{2}\), \(b = 3\)
Line 2: \(m = 1 = \frac{1}{1}\), \(b = -3\)
Check \((4, 1)\): \(1 = -\frac{1}{2}(4) + 3 = -2 + 3 = 1\) ✓ | \(1 = 4 - 3 = 1\) ✓
Problem 3 Solution: \((3, 0)\)
\(\begin{cases} \color{#2563eb}{y = \frac{2}{3}x - 2} \\ \color{#dc2626}{y = -x + 3} \end{cases}\)
Line 1: \(m = \frac{2}{3}\), \(b = -2\)
Line 2: \(m = -1\), \(b = 3\)
Check \((3, 0)\): \(0 = \frac{2}{3}(3) - 2 = 2 - 2 = 0\) ✓ | \(0 = -(3) + 3 = 0\) ✓
Problem 4 Solution: \((-2, 0)\)
\(\begin{cases} \color{#2563eb}{y = -2x - 4} \\ \color{#dc2626}{y = \frac{1}{2}x + 1} \end{cases}\)
Line 1: \(m = -2\), \(b = -4\)
Line 2: \(m = \frac{1}{2}\), \(b = 1\)
Check \((-2, 0)\): \(0 = -2(-2) - 4 = 4 - 4 = 0\) ✓ | \(0 = \frac{1}{2}(-2) + 1 = 0\) ✓
Crossing Lines • Teacher Answer Key Page 1 of 3
Crossing Lines Answer Key • Problems 5 to 7 Page 2 of 3
Problem 5 Solution: \((4, 2)\)
\(\begin{cases} \color{#2563eb}{y = \frac{3}{4}x - 1} \\ \color{#dc2626}{y = -\frac{1}{2}x + 4} \end{cases}\)
Line 1: \(m = \frac{3}{4}\), \(b = -1\)
Line 2: \(m = -\frac{1}{2}\), \(b = 4\)
Check \((4, 2)\):
\(2 = \frac{3}{4}(4) - 1 = 3 - 1 = 2\) ✓
\(2 = -\frac{1}{2}(4) + 4 = -2 + 4 = 2\) ✓
Problem 6 Solution: \((2, 0)\)
\(\begin{cases} \color{#2563eb}{2x + y = 4} \\ \color{#dc2626}{y = x - 2} \end{cases}\)
Line 1 conversion: \(2x + y = 4 \implies \mathbf{y = -2x + 4}\)
Slope \(m = -2\), \(y\)-intercept \((0, 4)\), \(x\)-intercept \((2, 0)\)
Line 2: Slope \(m = 1\), \(y\)-intercept \((0, -2)\)
Check \((2, 0)\):
\(2(2) + (0) = 4 + 0 = 4\) ✓ | \(0 = 2 - 2 = 0\) ✓
